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1
Farmer, Matthew Ray. "Applications in Fixed Point Theory." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4971/.
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Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.
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Sondjaja, Mutiara. "Sperner's Lemma Implies Kakutani's Fixed Point Theorem." Scholarship @ Claremont, 2008. https://scholarship.claremont.edu/hmc_theses/214.
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Kakutani’s fixed point theorem has many applications in economics and game theory. One of its most well known applications is in John Nash’s paper [8], where the theorem is used to prove the existence of an equilibrium strategy in n-person games. Sperner’s lemma, on the other hand, is a combinatorial result concerning the labelling of the vertices of simplices and their triangulations. It is known that Sperner’s lemma is equivalent to a result called Brouwer’s fixed point theorem, of which Kakutani’s theorem is a generalization. A natural question that arises is whether we can prove Kakutani’s fixed point theorem directly using Sperner’s lemma without going through Brouwer’s theorem. The objective of this thesis to understand Kakutani’s theorem, Sperner’s lemma, and how they are related. In particular, I explore ways in which Sperner’s lemma can be used to prove Kakutani’s theorem and related results.
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Niyitegeka, Jean Marie Vianney. "Generalizations of some fixed point theorems in banach and metric spaces." Thesis, Nelson Mandela Metropolitan University, 2015. http://hdl.handle.net/10948/5265.
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A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.
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Sendrowski, Janek. "Feigenbaum Scaling." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-96635.
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In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive.
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Nazaikinskii, Vladimir, Bert-Wolfgang Schulze, Boris Sternin, and Victor Shatalov. "A Lefschetz fixed point theorem for manifolds with conical singularities." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2507/.
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Cloutier, John. "A Combinatorial Analog of the Poincaré–Birkhoff Fixed Point Theorem." Scholarship @ Claremont, 2003. https://scholarship.claremont.edu/hmc_theses/145.
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Results from combinatorial topology have shown that certain combinatorial lemmas are equivalent to certain topologocal fixed point theorems. For example, Sperner’s lemma about labelings of triangulated simplices is equivalent to the fixed point theorem of Brouwer. Moreover, since Sperner’s lemma has a constructive proof, its equivalence to the Brouwer fixed point theorem provides a constructive method for actually finding the fixed points rather than just stating their existence. The goal of this research project is to develop a combinatorial analogue for the Poincare ́-Birkhoff fixed point theorem.
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Sracic, Mario F. "A Self-Contained Review of Thompson's Fixed-Point-Free Automorphism Theorem." Youngstown State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1403191722.
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BESBES, MOURAD. "Points fixes et theoremes ergodiques dans les espaces de banach." Paris 6, 1991. http://www.theses.fr/1991PA066034.
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Les deux questions principales etudiees dans cette these sont classiques en theorie du point fixe. La premiere concerne l'existence de points fixes pour une contraction non lineaire definie sur un convexe faiblement ou prefaiblement compact dans un espace de banach et la deuxieme structure de l'ensemble des points fixes d'une contraction lineaire ou non. On montre en particulier que certaines inegalites metriques, souvent faciles a verifier, suffisent pour montrer la structure normale faible ou prefaible. Ceci nous permet de retrouver d'une maniere tres simple certains resultats deja connus et de les generaliser. On montre aussi, pour certains espaces de banach, que l'ensemble des points fixes d'une contraction lineaire est contractivement complemente
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Sugiyama, Toshi. "The Moduli Space of Polynomial Maps and Their Fixed-Point Multipliers." Kyoto University, 2018. http://hdl.handle.net/2433/233819.
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Okon, Thomas. "When graph meets diagonal: an approximative access to fixed point theory." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2001. http://nbn-resolving.de/urn:nbn:de:swb:14-1000223151750-26347.
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Peterson, Elisha. "Combinatorial Proofs of Generalizations of Sperner's Lemma." Scholarship @ Claremont, 2000. https://scholarship.claremont.edu/hmc_theses/124.
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In this thesis, we provide constructive proofs of serveral generalizations of Sperner's Lemma, a combinatorial result which is equivalent to the Brouwer Fixed Point Theorem. This lemma makes a statement about the number of a certain type of simplices in the triangulation of a simplex with a special labeling. We prove generalizations for polytopes with simplicial facets, for arbitrary 3-polytopes, and for polygons. We introduce a labeled graph which we call a nerve graph to prove these results. We also suggest a possible non-constructive proof for a polytopal generalization.
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Garcia, Ignacio de Mateo. "Iterative matrix-free computation of Hopf bifurcations as Neimark-Sacker points of fixed point iterations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2012. http://dx.doi.org/10.18452/16478.
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Klassische Methoden für die direkte Berechnung von Hopf Punkten und andere Singularitaten basieren auf der Auswertung und Faktorisierung der Jakobimatrix. Dieses stellt ein Hindernis dar, wenn die Dimensionen des zugrundeliegenden Problems gross genug ist, was oft bei Partiellen Diferentialgleichungen der Fall ist. Die betrachteten Systeme haben die allgemeine Darstellung f ( x(t), α) für t grösser als 0, wobei x die Zustandsvariable, α ein beliebiger Parameter ist und f glatt in Bezug auf x und α ist. In der vorliegenden Arbeit wird ein Matrixfreies Schema entwicklet und untersucht, dass ausschliesslich aus Produkten aus Jakobimatrizen und Vektoren besteht, zusammen mit der Auswertung anderer Ableitungsvektoren erster und zweiter Ordnung. Hiermit wird der Grenzwert des Parameters α, der zuständig ist für das Verlieren der Stabilität des Systems, am Hopfpunkt bestimmt. In dieser Arbeit wird ein Gleichungssystem zur iterativen Berechnung des Hopfpunktes aufgestellt. Das System wird mit einer skalaren Testfunktion φ, die aus einer Projektion des kritischen Eigenraums bestimmt ist, ergänzt. Da das System f aus einer räumlichen Diskretisierung eines Systems Partieller Differentialgleichungen entstanden ist, wird auch in dieser Arbeit die Berechung des Fehlers, der bei der Diskretisierung unvermeidbar ist, dargestellt und untersucht. Zur Bestimmung der Hopf-Bedingungen wird ein einzelner Parameter gesteuert. Dieser Parameter wird unabhängig oder zusammen mit dem Zustandsvektor in einem gedämpften Iterationsschritt neu berechnet. Der entworfene Algorithmus wird für das FitzHugh-Nagumo Model erprobt. In der vorliegenden Arbeit wird gezeigt, wie für einen kritischen Strom, das Membranpotential eine fortschreitende Welle darstellt.Classical methods for the direct computation of Hopf bifurcation points and other singularities rely on the evaluation and factorization of Jacobian matrices. In view of large scale problems arising from PDE discretization systems of the form f( x (t), α ), for t bigger than 0, where x are the state variables, α are certain parameters and f is smooth with respect to x and α, a matrix-free scheme is developed based exclusively on Jacobian-vector products and other first and second derivative vectors to obtain the critical parameter α causing the loss of stability at the Hopf point. In the present work, a system of equations is defined to locate Hopf points, iteratively, extending the system equations with a scalar test function φ, based on a projection of the eigenspaces. Since the system f arises from a spatial discretization of an original set of PDEs, an error correction considering the different discretization procedures is presented. To satisfy the Hopf conditions a single parameter is adjusted independently or simultaneously with the state vector in a deflated iteration step, reaching herewith both: locating the critical parameter and accelerating the convergence rate of the system. As a practical experiment, the algorithm is presented for the Hopf point of a brain cell represented by the FitzHugh-Nagumo model. It will be shown how for a critical current, the membrane potential will present a travelling wave typical of an oscillatory behaviour.
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Galves, Ana Paula Tremura. "O teorema de Lefschetz-Hopf e sua relação com outros teoremas clássicos da topologia /." São José do Rio Preto : [s.n.], 2009. http://hdl.handle.net/11449/94208.
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Orientador: Maria Gorete Carreira AndradeBanca: Denise de Mattos
Banca: Ermínia de Lourdes Campello Fanti
Resumo: Em Topologia, mais especificamente em Topologia Algébrica, temos alguns resultados clássicos que de alguma forma estão relacionados. No desenvolvimento deste trabalho, estudamos alguns desses resultados, a saber: Teorema de Lefschetz-Hopf, Teorema do Ponto Fixo de Lefschetz, Teorema do Ponto Fixo de Brouwer, Teorema da Curva de Jordan e o Teorema Clássico de Borsuk-Ulam. Além disso, tivemos como objetivo principal mostrar relações existentes entre esses teoremas a partir do Teorema de Lefschetz-Hopf.
Abstract: In Topology, more specifically in Algebraic Topology, we have some classical results that are in some way related. In developing this work, we studied some of these results, namely the Lefschetz-Hopf Theorem, the Lefschetz Fixed Point Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem and the Classic Borsuk-Ulam Theorem. Moreover, our main objective was to show relationships among those theorems by using Lefschetz-Hopf Theorem.
Mestre
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Kang, Jinghong. "The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30435.
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This thesis deals with non-linear non-quadratic optimal
control problems in an autonomous system and a related
iterative numerical method, the Kleinman-Newton method,
for solving the problem. The thesis proves the local
convergence of Kleinman-Newton method using the contraction
mapping theorem and then describes how this Kleinman-Newton
method may be used to numerically solve for the optimal
control and the corresponding solution. In order to show the
proof and the related numerical work, it is necessary to
review some of earlier work in the beginning of Chapter 1
[Zhang], and to introduce the Kleinman-Newton method at the
end of the chapter. In Chapter 2 we will demonstrate the
proof. In Chapter 3 we will show the related numerical work
and results.Ph. D.
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Galves, Ana Paula Tremura [UNESP]. "O teorema de Lefschetz-Hopf e sua relação com outros teoremas clássicos da topologia." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/94208.
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Em Topologia, mais especificamente em Topologia Algébrica, temos alguns resultados clássicos que de alguma forma estão relacionados. No desenvolvimento deste trabalho, estudamos alguns desses resultados, a saber: Teorema de Lefschetz-Hopf, Teorema do Ponto Fixo de Lefschetz, Teorema do Ponto Fixo de Brouwer, Teorema da Curva de Jordan e o Teorema Clássico de Borsuk-Ulam. Além disso, tivemos como objetivo principal mostrar relações existentes entre esses teoremas a partir do Teorema de Lefschetz-Hopf.
In Topology, more specifically in Algebraic Topology, we have some classical results that are in some way related. In developing this work, we studied some of these results, namely the Lefschetz-Hopf Theorem, the Lefschetz Fixed Point Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem and the Classic Borsuk-Ulam Theorem. Moreover, our main objective was to show relationships among those theorems by using Lefschetz-Hopf Theorem.
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Albuquerque, Philipe Thadeo Lima Ferreira [UNESP]. "Ponto fixo: uma introdução no ensino médio." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/110607.
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000790735.pdf: 1590232 bytes, checksum: 5297d173df2a824606d944767eb1610c (MD5)O principal objetivo deste trabalho consiste na produção de um referencial teórico relacionado aos conceitos de ponto fixo, que possibilite, aos alunos do Ensino Médio, o desenvolvimento de habilidades e competências relacionadas à Matemática. Neste trabalho são colocadas abordagens contextualizadas e proposições referentes às noções de ponto fixo nas principais funções reais (afim, quadrática, modular, dentre outras) e sua interpretação geométrica. São abordados de maneira introdutória os conceitos do teorema do ponto fixo de Brouwer, o teorema do ponto fixo de Banach e o método de resolução de equações por aproximações sucessivas
The main objective of this work is to produce a theoretical concepts related to fixed point, enabling, for high school students, the development of skills and competencies related to Mathematics. This work placed contextualized approaches and proposals relating to notions of fixed point in the main real functions (affine, quadratic, modular, among others) and its geometric interpretation. Are approached introductory concepts of the fixed point theorem of Brouwer's, fixed point theorem of Banach and the method of solving equations by successive approximations
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Albuquerque, Philipe Thadeo Lima Ferreira de. "Ponto fixo : uma introdução no ensino médio /." São José do Rio Preto, 2014. http://hdl.handle.net/11449/110607.
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Orientador: German Jesus Lozada CruzBanca: Cosme Eustaquio Rubio Mercedes
Banca: Rita de Cássia Pavani Lamas
Resumo: O principal objetivo deste trabalho consiste na produção de um referencial teórico relacionado aos conceitos de ponto fixo, que possibilite, aos alunos do Ensino Médio, o desenvolvimento de habilidades e competências relacionadas à Matemática. Neste trabalho são colocadas abordagens contextualizadas e proposições referentes às noções de ponto fixo nas principais funções reais (afim, quadrática, modular, dentre outras) e sua interpretação geométrica. São abordados de maneira introdutória os conceitos do teorema do ponto fixo de Brouwer, o teorema do ponto fixo de Banach e o método de resolução de equações por aproximações sucessivas
Abstract: The main objective of this work is to produce a theoretical concepts related to fixed point, enabling, for high school students, the development of skills and competencies related to Mathematics. This work placed contextualized approaches and proposals relating to notions of fixed point in the main real functions (affine, quadratic, modular, among others) and its geometric interpretation. Are approached introductory concepts of the fixed point theorem of Brouwer's, fixed point theorem of Banach and the method of solving equations by successive approximations
Mestre
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Stötzner, Ailyn. "Optimal Control of Thermoviscoplasticity." Universitätsverlag der Technischen Universität Chemnitz, 2018. https://monarch.qucosa.de/id/qucosa%3A31887.
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This thesis is devoted to the study of optimal control problems governed by a quasistatic, thermoviscoplastic model at small strains with linear kinematic hardening, von Mises yield condition and mixed boundary conditions. Mathematically, the thermoviscoplastic equations are given by nonlinear partial differential equations and a variational inequality of second kind in order to represent the elastic, plastic and thermal effects.
Taking into account thermal effects we have to handle numerous mathematical challenges during the analysis of the thermoviscoplastic model, mainly due to the low integrability of the nonlinear terms on the right-hand side of the heat equation. One of our main results is the existence of a unique weak solution, which is proved by means of a fixed-point argument and by employing maximal parabolic regularity theory. Furthermore, we define the related control-to-state mapping and investigate properties of this mapping such as boundedness, weak continuity and local Lipschitz continuity. Another major result is the finding that the mapping is Hadamard differentiable; a main ingredient is the reformulation of the variational inequality, the so called viscoplastic flow rule, as a Banach space-valued ordinary differential equation with non-differentiable right-hand side. Subsequently, we consider an optimal control problem governed by thermoviscoplasticity and show the existence of a minimizer. Finally, close this thesis with numerical examples.Diese Arbeit ist der Untersuchung von Optimalsteuerproblemen gewidmet, denen ein quasistatisches, thermoviskoplastisches Model mit kleinen Deformationen, mit linearem kinematischen Hardening, von Mises Fließbedingung und gemischten Randbedingungen zu Grunde liegt. Mathematisch werden thermoviskoplastische Systeme durch nichtlineare partielle Differentialgleichungen und eine variationelle Ungleichung der zweiten Art beschrieben, um die elastischen, plastischen und thermischen Effekte abzubilden. Durch die Miteinbeziehung thermischer Effekte, treten verschiedene mathematische Schwierigkeiten während der Analysis des thermoviskoplastischen Systems auf, die ihren Ursprung hauptsächlich in der schlechten Regularität der nichtlinearen Terme auf der rechten Seite der Wärmeleitungsgleichung haben. Eines unserer Hauptresultate ist die Existenz einer eindeutigen schwachen Lösung, welches wir mit Hilfe von einem Fixpunktargument und unter Anwendung von maximaler parabolischer Regularitätstheorie beweisen. Zudem definieren wir die entsprechende Steuerungs-Zustands-Abbildung und untersuchen Eigenschaften dieser Abbildung wie die Beschränktheit, schwache Stetigkeit und lokale Lipschitz Stetigkeit. Ein weiteres wichtiges Resultat ist, dass die Abbildung Hadamard differenzierbar ist; Hauptbestandteil des Beweises ist die Umformulierung der variationellen Ungleichung, der sogenannten viskoplastischen Fließregel, als eine Banachraum-wertige gewöhnliche Differentialgleichung mit nichtdifferenzierbarer rechter Seite. Schließlich runden wir diese Arbeit mit numerischen Beispielen ab.
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Debbiche, Hanene. "Sur des problèmes de lubrification stationnaires et instationnaires non isothermes." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSES027/document.
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L’objectif de ce travail de thèse est d’étudier quelques problèmes elliptiques et paraboliques d’écoulement de fluides non Newtoniens incompressibles et non isothermes gouvernés par l’équation aux dérivées partielles de Stokes avec la condition de Tresca sur une partie du bord quand la viscosité dépend à la fois de la température, de la vitesse et du module du tenseur des taux de déformations. Dans le premier chapitre, on a fait une introduction générale. Dans le deuxième chapitre, nous nous intéressons au couplage entre le système de Stokes et l’équation de la chaleur en régime stationnaire. On montre l’existence de la solution de l’inéquation variationnelle décrivant le système de Stokes pour une température donnée quand la viscosité dépend à la fois de la température, de la vitesse et du module du tenseur des taux de déformations en utilisant la méthode de monotonie pour la vitesse et le théorème de De Rham pour la pression. Dans un deuxième temps, on étudie l’existence et l’unicité de la température solution de l’équation de la chaleur avec un terme L1(Ω) au second membre quand la viscosité dépend à la fois de la température, de la vitesse et du module du tenseur des taux de déformations. On montre ensuite l’existence de la solution du problème variationnel couplé avec la viscosité dépend de la température et du module du tenseur des taux de déformations, en utilisant le théorème de point fixe de Schauder. Dans le troisième et le quatrième chapitre, on traite l’existence et l’unicité de la solution du système de Stokes en régime instationnaire quand la viscosité dépend de la température et du module du tenseur des taux de déformations dans les cas p = 2, p > 2 et 6 5 < p < 2 en utilisant la notion des semi-groupes et la méthode de monotonie pour la vitesse et le théorème de De Rham pour la pression. Par contre, lorsque la viscosité dépend de plus de la vitesse on obtient seulement l’existence par le théorème de point fixe de SchauderThe objective of this thesis is to study some elliptic and parabolic problems of the non-Newtonian flow of an incompressible and non isothermal fluid governed by partial differential equation of Stokes with Tresca’s condition on a part of the boundary when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor and the velocity of the fluid. In the first chapter, we did a general introduction. In the second chapter, we consider the coupling between the Stokes systemand the heat equation in steady state. We prove the existence of a solution of the variational inequality describing the Stokes system when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor and the velocity of the fluid of a given temperature by using the monotony methods for the velocity and De Rham’s theorem for the pressure. We study the existence and uniqueness of the temperature solution of the heat equation with L1 (Ω) term to the second member when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor and the velocity of the fluid. We show the existence of a solution of the coupled variational problem when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor by using Schauder fixed point theorem. In the third and the fourth chapter, we treate the existence and uniqueness of a solution of the Stokes system in unsteady state when the fluid viscosity depends only on temperature and on the modulus of strain rate tensor in the cases p = 2, p > 2 and 6 5 < p < 2 by using the notion of semigroup and monotony methods for the velocity and De Rham’s theorem for the pressure. However, when the fluid viscosity depends also on the velocity of the fluid we obtain only the existence by Schauder fixed point theorem
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Rocha, Suelen de Souza. "Soluções clássicas para uma equação elíptica semilinear não homogênea." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/8051.
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This work is mainly concerned with the existence and nonexistence of classical solution to the nonhomogeneous semilinear equation Δu + up + f(x) = 0 in Rn, u > 0 in Rn, when n 3, where f 0 is a Hölder continuous function. The nonexistence of classical solution is established when 1 < p n=(n 2). For p > n=(n 2) there may be both existence and nonexistence results depending on the asymptotic behavior of f at infinity. The existence results were obtained by employed sub and supersolutions techniques and fixed point theorem. For the nonexistence of classical solution we used a priori integral estimates obtained via averaging.
Neste trabalho, estamos interessados na existência e não existência de solução clássica para a equação não homogênea semilinear Δu + up + f(x) = 0 em Rn; u > 0 em Rn, n 3 onde f 0 é uma função Hölder contínua. A não existência de solução clássica é estabelecida quando 1 < p n=(n 2). Para p > n=(n 2), temos resultados de existência e não existência de solução clássica, dependendo do comportamento assin- tótico de f no infinito. Os resultados de existência foram obtidos usando o método de sub e supersolução e teoremas de ponto fixo. A não existência de solução clássica é obtida usando-se estimativas integrais a priori via média esférica.
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LIMA, Annaxsuel Araújo de. "O método de sub e supersolução e aplicações a problemas elípticos." Universidade Federal de Campina Grande, 2011. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1241.
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Neste trabalho, apresentamos métodos envolvendo sub e supersolução para estudar a existência de solução de certas equações elípticas.
In this work, we present methods involving sub and supersolution to study the existence of solution of certain elliptic equations.
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Tang, Shun. "Le théorème de concentration et la formule des points fixes de Lefschetz en géométrie d’Arakelov." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112015/document.
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Dans les années quatre-vingts dix du siècle dernier, R. W. Thomason a démontréun théorème de concentration pour la K-théorie équivariante algébrique sur lesschémas munis d’une action d’un groupe algébrique G diagonalisable. Comme d’habitude,un tel théorème entraîne une formule des points fixes de type Lefschetz qui permetde calculer la caractéristique d’Euler-Poincaré équivariante d’un G-faisceau cohérent surun G-schéma propre en termes d’une caractéristique sur le sous-schéma des points fixes.Le but de cette thèse est de généraliser les résultats de R.W. Thomason dans le contextede la géométrie d’Arakelov. Dans ce travail, nous considérons les schémas arithmétiquesau sens de Gillet-Soulé et nous tout d’abord démontrons un analogue arithmétiquedu théorème de concentration pour les schémas arithmétiques munis d’une action duschéma en groupe diagonalisable associé à Z/nZ. La démonstration résulte du théorèmede concentration algébrique joint à des arguments analytiques. Dans le dernier chapitre,nous formulons et démontrons deux types de formules de Lefschetz arithmétiques. Cesdeux formules donnent une réponse positive à deux conjectures énoncées par K. Köhler,V. Maillot et D. RösslerIn the nineties of the last century, R. W. Thomason proved a concentrationtheorem for the algebraic equivariant K-theory on the schemes which are endowed withan action of a diagonalisable group scheme G. As usual, such a concentration theoreminduces a fixed point formula of Lefschetz type which can be used to calculate theequivariant Euler-Poincaré characteristic of a coherent G-sheaf on a proper G-schemein terms of a characteristic on the fixed point subscheme. It is the aim of this thesis togeneralize R. W. Thomason’s results to the context of Arakelov geometry. In this work,we consider the arithmetic schemes in the sense of Gillet-Soulé and we first prove anarithmetic analogue of the concentration theorem for the arithmetic schemes endowedwith an action of the diagonalisable group scheme associated to Z/nZ. The proof is acombination of the algebraic concentration theorem and some analytic arguments. Inthe last chapter, we formulate and prove two kinds of arithmetic Lefschetz formulae.These two formulae give a positive answer to two conjectures made by K. Köhler, V.Maillot and D. Rössler
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SILVA, Geizane Lima da. "Soluções blow-up para uma classe de equações elípticas." Universidade Federal de Campina Grande, 2010. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1231.
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Capes
Neste trabalho estudamos a existência de soluções positivas do tipo blow-up para uma classe de equações elípticas semilineares. Usamos argumentos desenvolvidos por Cîrstea & Radulescu [6], Lair & Wood [20] e as técnicas empregadas são o Método de Sub e Supersolução, Teoremas de Ponto Fixo e em alguns resultados exploramos a simetria radial e algumas estimativas para equações elípticas.
In this work we studied the existence of blow-up positive solutions for the class of semilinear elliptic equations. We used arguments developed by Cîrstea & Radulescu [6], and by Lair & Shaker [20] and the techniques used are the method of Sub and Supersolution, Fixed point theorems and some results explored radial symmetry and some estimates for elliptic equations.
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Ayed, Hela. "Analyse d'un problème d'interaction fluide-structure avec des conditions aux limites de type frottement à l'interface." Thesis, Normandie, 2017. http://www.theses.fr/2017NORMC213/document.
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Cette thèse est consacrée à l'analyse mathématique et numérique d'un problème d'interaction fluide-structure stationnaire, couplant un fluide newtonien, visqueux et incompressible, modélisé par les équations de Stokes 2D et une structure déformable, décrite par les équations d'une poutre 1D. Le fluide et la structure sont couplés via une condition aux limites de type frottement à l'interface.Dans l'étude théorique, nous montrons un résultat d'existence et unicité de solutions faibles, dans le cadre de petits déplacements, du problème de couplage fluide structure avec une condition de glissement de type Tresca en utilisant le théorème de point fixe de Schauder.Dans l'analyse numérique, nous étudions d'abord, l'approximation du problème de Stokes avec la condition de Tresca par une méthode d'éléments finis mixtes à quatre champs. Nous montrons ensuite une estimation d'erreur a priori optimale pour des données régulières et nous réalisons des tests numériques. Enfin, nous présentons un algorithme de point fixe pour la simulation numérique du problème couplé avec des conditions aux limites non linéairesThis PHD thesis is devoted to the theoretical and numerical analysis of a stationary fluid-structure interaction problem between an incompressible viscous Newtonian fluid, modeled by the 2D Stokes equations, and a deformable structure modeled by the 1D beam equations.The fluid and structure are coupled via a friction boundary condition at the fluid-structure interface.In the theoretical study, we prove the existence of a unique weak solution, under small displacements, of the fluid-structure interaction problem under a slip boundary condition of friction type (SBCF) by using Schauder fixed point theorem.In the numerical analysis, we first study a mixed finite element approximation of the Stokes equations under SBCF.We also prove an optimal a priori error estimate for regular data and we provide numerical examples.Finally, we present a fixed point algorithm for numerical simulation of the coupled problem under nonlinear boundary conditions
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SANTOS, Joselma Soares dos. "Soluções de sistemas de equações diferenciais elípticas via Teoria de ponto fixo em cones." Universidade Federal de Campina Grande, 2007. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1183.
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Neste trabalho usaremos a Teoria do Ponto fixo em Cones para provar a existência e multiplicidade de solução positiva radial para sistemas de equações diferenciais parciais elípticas de segunda ordem onde 0 < r1 < r2 e a,b são parâmetros não-negativos. * (O resumo original da dissertação aprenta um sistema de equação que não foi possível adiciona-lo aqui. Recomendamos o download do arquivo para acessoao resumo completo)
In this work we will use the Theory of the Fixed Point in Cones to prove the existence and multiplicity of positive solutions for systems of second-ordem elliptic differential equations where 0 < r1 < r2 and a,b are non-negative parameters. * (The original abstract of the dissertation presents an equation system that could not be added here. We recommend downloading the file for access to the full summary)
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He, Yuan. "Analyse et contrôle de modèles de dynamique de populations." Thesis, Bordeaux 1, 2013. http://www.theses.fr/2013BOR14918/document.
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La présente thèse est divisée en deux parties. La première partie concerne l'analyse mathématique et la contrôlabilité exacte à zéro pour une catégorie de systèmes structurés décrivant la dynamique d'une population d'insectes. La seconde partie est consacrée à l'étude de la stabilité de la conductivité d'un système de réaction diffusion modélisant l'activité électrique du coeur.Dans le chapitre 2, on considère que la population d'adultes se diffuse dans la vignoble,la fonction de la croissance des individus à chaque stade dépend des variations climatiques et de la variété des raisins. En utilisant la méthode de point fixe, on obtient l'existence et l'unicité des solutions du modèle. On démontre ensuite l'existence d'un attracteur global pour le système dynamique. Enfin, on utilise la théorie des opérateurs compacts et le théorème de point fixe de Krasnoselskii pour prouver l'existence des états stationnaires.Dans le chapitre 3, on traite le problème de contrôlabilité exacte du modèle de Lobesia Botrana, lorsque la fonction de croissance est égale à 1. On suppose que les quatre sous-catégories de ce système sont dans une phase statique. On obtient que la population d'oeufs peut être contrôlée à zéro. Ce résultat est basé sur des estimations à priori combinées avec un théorème de point fixe.Lorsque les papillons adultes se dispersent spatialement, on introduit un contrôle sur la population d'oeufs, de larves et de femelles dans une petite région du vignoble. On montre alors la contrôlabilité exacte à zéro pour les femelles.Dans la deuxième partie de cette thèse, on analyse la stabilité des coefficients de diffusion d'un système parabolique qui modélise l'activité électrique du coeur. On établit une estimation de Carleman pour le système de réaction-diffusion. En combinant cette estimation avec des estimations d'énergie avec poids on obtient le résultat de stabilitéThis thesis is divided into two parts.One is mainly devoted to make a qualitative analysis and exact null controlfor a class of structured population dynamical systems, and the other concernsstability of conductivities in an inverse problem of a reaction-diffusion systemarising in electrocardiology.In the first part, we study the dynamics ofEuropean grape moth, which has caused serious damages on thevineyards in Europe,North Africa, and even some Asian countries.To model this grapevine insect, physiologically structured multistage population systems are proposed.These systemshave nonlocal boundary conditions arising in nonlocal transition processes in ecosystem.We consider the questions of spatial spread of the populationunder physiological age and stage structures,and show global dynamical properties for the model.Furthermore, we investigate the control problem for this Lobesia botrana modelwhen the growth function is equal to $1$.For the case that four subclasses of this system are all in static station,we conclude that the population of eggs can be controlled to zero at acertain moment by acting on eggs.While the adult moths can disperse,we describe a control by a removal of egg and larvapopulation, and also on female moths in a small region of the vineyard.Then the null controllability for female mothsin a nonempty open sub-domain at a given time is obtained.In the second part, a reaction-diffusion system approximating a parabolic-elliptic systemwas proposed tomodel electrical activity in the heart. We are interested inthe stability analysis of an inverse problem for this model.Then we use the method of Carleman estimates and certain weight energyestimatesfor the identification of diffusion coefficients for the parabolicsystem to draw the conclusion
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Moreira, Ceilí Marcolino. "O método de sub e supersoluções para soluções fracas." Universidade Federal de Juiz de Fora (UFJF), 2014. https://repositorio.ufjf.br/jspui/handle/ufjf/4702.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho, apresentamos métodos envolvendo sub e supersolução para estudar a existência de solução, no sentido fraco, para três classes de problemas elípticos de segunda ordem com condição de fronteira de Dirichlet homogênea. Nos dois primeiros casos encontramos solução em W1,2 0 (Ω) e no terceiro caso encontramos solução em L1(Ω) com algumas restrições.
This paper presents methods involving sub and supersolution in order to learn the existence of weak solutions of three classes of second order elliptic problems with homogeneous Dirichlet boundary conditions. In the first two cases we find solution in W1,2 0 (Ω) and in the third case we find solution in L1(Ω) with some restrictions.
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ALMEIDA, Orlando Batista de. "Teoria do Grau e aplicações." Universidade Federal de Campina Grande, 2006. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1139.
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Nesta dissertação, seguindo o trabalho do Berestycki [7] e idéias desenvolvidas por Alves & de Figueiredo [3] e Alves, Corrêa & Gonçalves [4], estudamos a Teoria do Grau de Brouwer e Leray & Schauder, bem como o Método de Galerkin para obter solução de alguns problemas elípticos.
In this of dissertation, motivated by work of Berestycki [7] and ideas conceived byAlves & from Figueiredo [3] andAlves, Corrêa & Gonçalves [4], we styding the theory of Degree fromBrouwer and Leray & Schauder, well how theMethod from Galerkin to obtain solution of some ellíptic problems.
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VIEIRA, Francisca Leidmar Josué. "Sobre a existência de soluções estacionárias para um sistema de reação-difusão." Universidade Federal de Campina Grande, 2009. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1209.
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Capes
O resumo foi escrito utilizando formulas e equações matemáticas que não fora possíveis serem transcritas aqui. Para a visualizar o resumo recomendamos o downloado do arquivo.
The abstract was written using mathematical formulas and equations that could not be transcribed here. To view the summary we recommend downloading the file.
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Ndao, Mamadou. "Estimation de la vitesse de retour à l'équilibre dans les équations de Fokker-Planck." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLV036/document.
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Ce mémoire de thèse est consacré à l’équation de Fokker-Planckpartial_ f=∆f+div(Ef).Il est subdivisé en deux parties :une partie linéaire et une partie non linéaire. Dans la partie linéaire on considère un champ de vecteur E(x) dépendant seulement de x. Cette partie est constituée des chapitres 3, 4 et 5. Dans le chapitre 3 on montre que l’opérateur linéaire Lf :=∆ f + div(E f ) est le générateur d’un semi-groupe fortement continu (SL(t))_{t≥0} dans tous les espaces L^p. On y établit également que le semi-groupe (SL(t))_{t≥0} est positif et ultracontractif. Dans le chapitre 4 nous montrons comment est qu’une décomposition adéquate de l’opérateur L permet d’établir certaines propriétés du semi-groupe (SL(t))_{t≥0} notamment sa bornitude. Le chapitre 5 est consacré à l’existence d’un état d’équilibre. De plus on y montre que cet état d’équi- libre est asymptotiquement stable. Dans la partie non linéaire on considère un champ de vecteur de la forme E(x,f) := x+nabla (a*f) ou a et f sont des fonctions assez régulières et * est l’opérateur de convolution. Cette parties est contituée des chapitre 6 et 7. Dans le chapitre 6 nous établissons que poura appartenant à W^{2,infini}_locl’équation de Fokker-Planck non linéaire admet une unique solution locale dans l’espace L^2_{K_alpha} (R^d). Dans le dernier chapitre nous montrons que le problème non linéaire admet une solution globale. De plus cette solution dépend continument des donnéesThis thesis is devoted to the Fokker-Planck équation partial_t f =∆f + div(E f).It is divided into two parts. The rst part deals with the linear problem. In this part we consider a vector E(x) depending only on x. It is composed of chapters 3, 4 and 5. In chapter 3 we prove that the linear operator Lf :=∆f + div(Ef ) is an in nitesimal generator of a strong continuous semigroup (SL(t))_{t≥0}. We establish also that (SL(t))_{t≥0} is positive and ultracontractive. In chapter 4 we show how an adequate decomposition of the linear operator L allows us to deduce interesting properties for the semigroup (SL(t))_{t≥0}. Indeed using this decomposition we prove that (SL(t))_{t≥0} is a bounded semigroup. In the last chapter of this part we establish that the linear Fokker-Planck admits a unique steady state. Moreover this stationary solution is asymptotically stable.In the nonlinear part we consider a vector eld of the form E(x, f ) := x +nabla (a *f ), where a and f are regular functions. It is composed of two chapters. In chapter 6 we establish that fora in W^{2,infini}_locthe nonlinear problem has a unique local solution in L^2_{K_alpha}(R^d); . To end this part we prove in chapter 7 that the nonlinear problem has a unique global solution in L^2_k(R^d). This solution depends continuously on the data
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Vážanová, Gabriela. "Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2020. http://www.nusl.cz/ntk/nusl-433560.
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Dizertační práce se věnuje funkcionálním diferenciálním rovnicím smíšeného typu. Poskytuje kritéria pro existenci globálních a semi-globálních řešení diferenciálních systémů smíšeného typu. Metody použité v teto práci spočívají v sestavení vhodných operátorů pro diferenciální rovnice a prokázání existence jejich pevných bodů. Tyto pevné body jsou potom použity ke konstrukci řešení rovnic s předcházením a zpožděním. V důkazech tvrzení jsou použity monotónní iterační metoda a Schauderovy-Tychonovovy věty o existenci pevného bodu. V obou případech jsou uvedeny také odhady řešení. Pokud je použita iterační metoda, lze tyto odhady zlepšit iterováním. Kromě toho jsou odvozena kritéria pro lineární rovnice a systémy a je uvedena řada přikladů. Dosažené výsledky lze aplikovat také pro obyčejné diferenciální rovnice nebo diferenciální rovnice se zpožděním či s předcházením argumentu.
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Karliczek, Martin. "Elements of conditional optimization and their applications to order theory." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/17085.
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In dieser Arbeit beweisen wir für Optimierungsprobleme in L0-Moduln relevante Resultate und untersuchen Anwendungen für die Darstellung von Präferenzen. Im ersten Kapitel geht es um quasikonkave, monotone und lokale Funktionen von einem L0-Modul X nach L0, die wir robust darstellen. Im zweiten Kapitel entwickeln wir das Ekeland’sche Variationsprinzip für L0-Moduln, die eine L0-Metrik besitzen. Wir beweisen eine L0 -Variante einer Verallgemeinerung des Ekeland’schen Theorems. Der Beweis des Brouwerschen Fixpunktsatzes für Funktionen, die auf (L0)^d definiert sind, wird in Kapitel 3 behandelt. Wir definieren das Konzept des Simplexes in (L0)^d und beweisen, dass jede lokale, folgenstetige Funktion darauf einen Fixpunkt besitzt. Dies nutzen wir, um den Fixpunktsatz auch für Funktionen auf beliebigen abgeschlossenen, L0 -konvexen Mengen zu zeigen. Eine allgemeinere Struktur als L0 ist die bedingte Menge. Im vierten Kapitel behandeln wir bedingte topologische Vektorräume. Wir führen das Konzept der Dualität für bedingte Mengen ein und beweisen Theoreme der Funktionalanalysis darauf, unter anderem das Theorem von Banach-Alaoglu und Krein-Šmulian. Im fünften Kapitel widmen wir uns der Darstellung mit wandernden konvexen Mengen. Wir zeigen danach, wie die Transitivität für diese Darstellungsform beschrieben werden kann. Abschließend modellieren wir die Eigenschaft, dass die Transitivität einer Relation nur für ähnliche Elemente gesichert ist und diskutieren Arten der Darstellung solcher Relationen.In this thesis, we prove results relevant for optimization problems in L0-modules and study applications to order theory. The first part deals with the notion of an Assessment Index (AI). For an L0 -module X an AI is a quasiconcave, monotone and local function mapping to L0. We prove a robust representation of these AIs. In the second chapter of this thesis, we develop Ekeland’s variational principle for L0-modules allowing for an L0-metric. We prove an L0-Version of a generalization of Ekeland’s theorem. A further application of L0 -theory is examined in the third chapter of this thesis, namely an extension of the Brouwer fixed point theorem to functions on (L0)^d . We define a conditional simplex, which is a simplex with respect to L0 , and prove that every local, sequentially continuous function has a fixed point. We extend the fixed point theorem to arbitrary closed, L0-convex sets. A more general structure than L0 -modules is the concept of conditional sets. In the fourth chapter of the thesis, we study conditional topological vector spaces. We examine the concept of duality for conditional sets and prove results of functional analysis: among others, the Banach-Alaoglu and the Krein-Šmulian theorem. Any L0 -module being a conditional set allows to apply all results to L0 -theory. In the fifth chapter, we discuss the property of transitivity of relations and its connection to certain forms of representations. After a survey of common representations of preferences, we attend to relations induced by moving convex sets which are relations of the form that x is preferred to y if and only if x − y is in a convex set depending on y. We examine in which cases such a representation is transitive. Finally, we exhibit nontransitivity due to dissimilarity of the compared object and discuss representations for relations of that type.
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Huang, Yuh Jen, and 黃玉珍. "Fixed Point Theorem." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/33678969995411897390.
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CAI, XU-CHEN, and 蔡旭琛. "Fixed point theorem." Thesis, 1988. http://ndltd.ncl.edu.tw/handle/82411347389419920008.
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姜淑梅. "Fixed point theorem, cycle point theorems and their applications." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/08929230492999461471.
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碩士國立新竹教育大學
人資處數學教育碩士班
94
Abstract In this paper, we establish a fixed theorem of a and apply this fixed theorem to get an existence theorem concerning generalized variational inequalities. We also establish some cycle point theorems for three set-valued mappings. (特殊符號無法顯現請參閱PDF檔)
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Lin, Su-chin, and 林素貞. "A FIXED POINT THEOREM IN MENGER SPACES." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/88418895357133060333.
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碩士國立新竹教育大學
進修部數理教育碩士班(數學組)
92
In this paper, we prove a fixed point theorem for set-valued mapping from a Menger space (X, □, t) into K(X) with a contractive condition. This fixed point theorem is a new result about Hausdorff measure on Menger space.
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Kao, Lien-Yung, and 高連庸. "A Survey Of Poincare-Birkhoff Fixed Point Theorem." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/86225291482813380620.
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碩士臺灣大學
數學研究所
98
This paper further modifies Brown and Neumann’s proof to make it as clear as possible, clarifying what the previous renditions have left unclear.Moreover, the periodic trajectories problem of billiard is chosen as a application of the Poincare-Birkhoff fixed point theorem.
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Tang, Fu-Sheng, and 湯富勝. "A generalization of Brezis-Browder’s fixed point theorem for set-valued functionsA generalization of Brezis-Browder’s fixed point theorem for set-valued functionsA generalization of Brezis-Browder’s fixed point theorem for set-valued functionsA gene." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/cqsp97.
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碩士國立台北師範學院
數學暨資訊教育學系(含數學教育碩士班)
93
We consider the bounded above and upper semicontinuous functions on complete metric spaces. We establish some results about set-valued mapping, and apply them to established some fixed points of set-valued mapping, which are generalizations of those in Caristi [2].
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Chang, Li-Chien, and 張豊傑. "A common fixed point theorem in compact menger spaces." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/06189470866136944608.
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碩士國立新竹教育大學
進修部數理教育碩士班(數學組)
92
In the paper we prove a contractive type common fixed point theorem for four self-mappings in a Menger space （X,F,t ） . This theorem in fact extends some results of common fixed point theorems for the case that X is a metric space.
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LI-CHIEH, CHANG, and 張豊傑. "A COMMON FIXED POINT THEOREM IN COMPACT MENGER SPACES." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/75478440562978738857.
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碩士國立新竹師範學院
數理教育碩士班數學組
92
In the paper we prove a contractive type common fixed point theorem for four self-mappings in a Menger space（ F, ）. This theorem in fact extends some results of common fixed point theorems for the case that X is a metric space.
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LIN, CHIH-YEN, and 林志彥. "A Study of Brouwer's Fixed Point Theorem and Nash's Equilibrium." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/00776892857036802768.
Full textAbstract:
碩士中原大學
應用數學研究所
95
The purpose of this thesis is to give a detail study of the well known Brouwer's fixed point theorem and Nash's equilibrium theorem. Section 1 is an introduction. Notions about triangulations of simplexes are recalled in section 2, the definitions of the affine independence, affne combination, affine hull, convex hull, barycentric coordinate, simplex, face, and triangulation are given and some basic properties of them are listed. In section 3, the definitions of barycenters of simplexes and sequences of ascending simplexes are introduced. After some discussions, the existence of a triangulation, the k-th barycentric subdivision, of a simplex is established, in case k is large enough, the maximum diameter of its members can be arbitrarily small. In section 4, we study some topological properties of convex sets and convex bodies, we see that some special homeomorphisms map convex bodies onto simplexes of suitable dimensions. In section 5, we study the celebrate theorems of Sperner, Knaster-Kuratowski-Mazurkiewicz, and Brouwer in a typical way. In section 6, the definition of noncooperative finite games in normal form is given, notions of the player, pure or mixed strategy, situation, payoff and equilibrium point are introduced with some examples. We see that the fixed points of Nash mappings are exactly the equilibrium points in mixed strategies of the corresponding games.
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羅錫康. "A Common Fixed Point Theorem in Complete G-Metric Spaces." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/28083360650483600229.
Full textAbstract:
碩士國立新竹教育大學
應用數學系碩士班
98
In this paper, we prove some coincidence points for mapping satisfying (CBW) conditions on complete G-Metric Spaces, also we showed if mappings f and g are commute at their coincidence points, then they have a common fixed point result.
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Lin, Ya-Ting, and 林雅婷. "A Common Fixed Point Theorem in Cone Rectangular Metric Spaces." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/54054991222959575768.
Full textAbstract:
碩士國立新竹教育大學
應用數學系碩士班
98
Abstract In this paper, we first introduce the function phi which satisfies the condition (CBW), and then prove a common fixed point theorem in a cone rectangular metric space.
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"Combinatorial analogs of Brouwer's fixed point theorem on a bounded polyhedron." Massachusetts Institute of Technology, Alfred P. Sloan School of Management, 1985. http://hdl.handle.net/1721.1/2126.
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陳榴明. "COMMON FIXED POINT THEOREM FOR SET-VALUED MAPPINGS IN MENGER SPACES." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/04898075478171543425.
Full textAbstract:
碩士國立新竹教育大學
進修部數理教育碩士班(數學組)
92
In this paper, we shall prove a common fixed point theorem in probabilistic metric space of set-valued functions with -contractive condition, which generalize some results of V.M. Sehgal & A.T. Bharucha-Reid [12].
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Wu, Shu-Han, and 吳樹恆. "Generalization of Shih-Dong's combinational fixed point theorem to finite distributive lattices." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/09311531637943657275.
Full textAbstract:
博士國立臺灣師範大學
數學系
103
Shih-Dong's combinational fixed point theorem asserts that if a map from the n-dimensional hypercube into itself satisfies that all the Boolean eigenvalues of the Boolean Jacobian matrix are zero for each element in the hypercube, then it has a unique fixed point. Its equivalent contrapositive form has biological implications. Our goal is to provide an extension of Shih-Dong's theorem into all finite distributive lattices. Our method of proof is based on Shih-Dong's “collective effect method” as well as G. Birkhoff's representation theorem for finite distributive lattices.
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Huilin-Cheng and 鄭蕙琳. "A Study of Fixed Point Theorem and Related Theorems for Compact Convex Sets." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/14693189141574874552.
Full textAbstract:
碩士中原大學
數學系
88
The purpose of this master’s thesis is to study Ky Fan’s minimax inequality [3], which gives a new proof to the unification of Nash’s equilibrium point theorem [6] and Von Neumann’s minimax principle [9] that was raised by Ky Fan [2]. It also has broad usage [3] in many fields. Von Neumann’s minimax principle [9] indicates the conditions that a two-person zero-sum game has a saddle point and Nash’s equilibrium point theorem [6] indicates the conditions that n-person non-cooperative game has a Nash’s equilibrium point. Although in two-person zero-sum game, Nash’s equilibrium point has the same meaning as the saddle point, Nash’s equilibrium point theorem is not an extension of Von Neumann’s minimax principle because its demandable conditions are stronger. In 1964, Ky Fan gave a common generalization [2] of Nash’s equilibrium point theorem and Von Neumann’s minimax principle. Furthermore, an extensive used theorem─Ky Fan’s minimax inequality [3] was published in 1972, which, of course, implies his previous result. Ky Fan’s minimax inequality is an inevitable result of real valued functions, which satisfies some particular conditions. In this thesis, we find it will be more natural to extend these functions to extended real valued functions. The body of this thesis was divided to three parts. The first part is preliminaries, it introduces definitions, terminologies and results that will be used in the thesis, then we use Brouwer fixed point theorem to prove Knaster-Kuratowski-Mazurkiewicz theorem [5] and Ky Fan’s generalization [1]. In the end of the first part, we give a detailed discussion of semicontinuity and quasiconvexity of extended real valued functions for the preparation of the last part of this thesis. Then, in the last part, we first prove Ky Fan’s two results for extended real valued functions and then prove Nash’s equilibrium point theorem and Von Neumann’s minimax principle by applying Ky Fan’s results. In the end of this thesis, we give an example to show that it will be better to discuss the Ky Fan’s minimax inequality by considering extended real number system.
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Shih, Cyuan-Jhe, and 施權哲. "Fixed point theorem for the cyclic Meir-Keeler contractions on metric-like spaces." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/97408838408190719410.
Full textAbstract:
碩士國立新竹教育大學
應用數學系碩士班
104
In this article, by using the cyclic represtation and Meir-Keeler type mappings, we introduce two kinds of cyclic Meir-Keeler type contractions and then establish some new fixed theorems for these cyclic Meir-Keeler type contractions defined on a metric-like space X with a cyclic represen tation of X. Our results generalize and improve many recent fixed point theorems for generalized cyclic contractive mappings in the literature.
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Wu, Chien-Lung, and 吳建龍. "Fixed Point Theorem of Uniformly Locally Geraghty Contractive Mappings on Connected Complete Metric Spaces." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/86818039267794315774.
Full textAbstract:
碩士國立高雄師範大學
數學系
105
In this paper, we first introduce the concept of uniformly locally contractive mapping. Second, complete metric space is modified to be a connected complete metric space. Third, Our generalization of the Banach contraction principle replaces the global contraction hypothesis with the local contraction hypothesis. Then we investigate the behavior for mappings satisfying uniformly locally Geraghty contraction on connected complete metric space. Finally, we establish a new existence and uniqueness result of fixed point theorem.
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Chiu, Yung-Nan, and 邱永男. "Some new generalizations of Mizoguchi-Takahashi's fixed point theorem with local constraints and their applications." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/68788729030880244622.
Full textAbstract:
碩士國立高雄師範大學
數學系
103
In this paper, motivated by Kikkawa-Suzuki's xed point theorem, we rst estab- lish some new generalizations of Mizoguchi-Takahashi's xed point theorem with new local constraints on discussion maps. As applications of our results, some new xed point theorems are given.