Relevant bibliographies by topics / Banach's fixed point theorem

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Banach's fixed point theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Banach's fixed point theorem"

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Brzdęk, Janusz, Liviu Cădariu, and Krzysztof Ciepliński. "Fixed Point Theory and the Ulam Stability." Journal of Function Spaces 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/829419.

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The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.
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Subrahmanyam, P. V., and I. L. Reilly. "Some fixed point theorems." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 3 (December 1992): 304–12. http://dx.doi.org/10.1017/s144678870003648x.

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AbstractBanach's contraction principle guarantees the existence of a unique fixed point for any contractive selfmapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach's theorem carry over to spaces whose topologies are generated by families of quasi-pseudometrics.
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Zima, M. "A certain fixed point theorem and its applications to integral-functional equations." Bulletin of the Australian Mathematical Society 46, no. 2 (October 1992): 179–86. http://dx.doi.org/10.1017/s0004972700011813.

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In this paper a variant of Banach's contraction principle is established. By using the properties of the spectral radius of a bounded linear operator A defined in a suitable Banach space, we conclude that another operator A has exactly one fixed point in this space. In the second part of this paper some applications are given.
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Hicks, Troy L. "Fixed point theorems ford-complete topological spaces I." International Journal of Mathematics and Mathematical Sciences 15, no. 3 (1992): 435–39. http://dx.doi.org/10.1155/s0161171292000589.

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Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These included-complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.
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Bouzaroura, Asma, and Saïd Mazouzi. "An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space." International Journal of Differential Equations 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/191060.

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This paper is concerned with the existence, uniqueness, and stability of the solution of some impulsive fractional problem in a Banach space subjected to a nonlocal condition. Meanwhile, we give a new concept of a solution to impulsive fractional equations of multiorders. The derived results are based on Banach's contraction theorem as well as Schaefer's fixed point theorem.
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Sangurlu, S. M., and D. Turkoglu. "Some fixed point results in complete generalized metric spaces." Carpathian Mathematical Publications 9, no. 2 (January 2, 2018): 171–80. http://dx.doi.org/10.15330/cmp.9.2.171-180.

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The Banach contraction principle is the most important result. This principle has many applications and some authors was interested in this principle in various metric spaces as Brianciari. The author initiated the notion of the generalized metric space as a generalization of a metric space by replacing the triangle inequality by a more general inequality, $d(x,y)\leq d(x,u)+d(u,v)+d(v,y)$ for all pairwise distinct points $x,y,u,v$ of $X$. As such, any metric space is a generalized metric space but the converse is not true. He proved the Banach fixed point theorem in such a space. Some authors proved different types of fixed point theorems by extending the Banach's result. Wardowski introduced a new contraction, which generalizes the Banach contraction. He using a mapping $F: \mathbb{R}^{+} \rightarrow \mathbb{R}$ introduced a new type of contraction called $F$-contraction and proved a new fixed point theorem concerning $F$-contraction. In this paper, we have dealt with $F$-contraction and $F$-weak contraction in complete generalized metric spaces. We prove some results for $F$-contraction and $F$-weak contraction and we show that the existence and uniqueness of fixed point for satisfying $F$-contraction and $F$-weak contraction in complete generalized metric spaces. Some examples are supplied in order to support the useability of our results. The obtained result is an extension and a generalization of many existing results in the literature.
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Yan, Zuomao. "On solutions of semilinear evolution integrodifferential equations with nonlocal conditions." Tamkang Journal of Mathematics 40, no. 3 (September 30, 2009): 257–69. http://dx.doi.org/10.5556/j.tkjm.40.2009.505.

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In this paper, by using the theory of evolution families, Banach's contraction principle and Schauder's fixed point theorem, we prove the existence of mild solutions of a class of semilinear evolution integrodifferential equations with nonlocal conditions in Banach space. An example is provided to illustrate the obtained results.
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DECK, THOMAS. "CONTINUOUS DEPENDENCE ON INITIAL DATA FOR SOLUTIONS OF NONLINEAR STOCHASTIC EVOLUTION EQUATIONS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, no. 03 (September 2002): 333–50. http://dx.doi.org/10.1142/s0219025702000870.

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We consider stochastic evolution equations in the framework of white noise analysis. Contraction operators on inductive limits of Banach spaces arise naturally in this context and we first extend Banach's fixed point theorem to this type of spaces. In order to apply the fixed point theorem to evolution equations, we construct a topological isomorphism between spaces of generalized random fields and the corresponding spaces of U-functionals. As an application we show that the solutions of some nonlinear stochastic heat equations depend continuously on their initial data. This method also applies to stochastic Volterra equations, stochastic reaction–diffusion equations and to anticipating stochastic differential equations.
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de Bakker, J. W., and E. P. de Vink. "Denotational models for programming languages: applications of Banach's Fixed Point Theorem." Topology and its Applications 85, no. 1-3 (May 1998): 35–52. http://dx.doi.org/10.1016/s0166-8641(97)00140-5.

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Adamek, J., and J. Reiterman. "Banach's Fixed-Point Theorem as a base for data-type equations." Applied Categorical Structures 2, no. 1 (1994): 77–90. http://dx.doi.org/10.1007/bf00878504.

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Dissertations / Theses on the topic "Banach's fixed point theorem"

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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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Books on the topic "Banach's fixed point theorem"

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Cai, Zongxi. Deng zhou wen ti. Beijing: Ke xue chu ban she, 2002.

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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Fixed Point Buildings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0022.

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This chapter presents the proof for the Fundamental Theorem of Descent in buildings: that if Γ‎ is a descent group, the set of residues of a building Δ‎ that are stabilized by a subgroup Γ‎ of Aut(Γ‎) forms a thick building. It begins with the hypothesis: Let Π‎ be an arbitrary Coxeter diagram, let S be the vertex set of Π‎ and let (W, S) be the corresponding Coxeter system. It then defines a Γ‎-residue and a Γ‎-chamber as well as a descent group of Δ‎ before concluding with the main result about the fixed point building of Γ‎.
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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Affine Fixed Point Buildings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0027.

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This chapter shows that if Ξ‎ is an affine building and Γ‎ is a finite descent group of Ξ‎, then Γ‎ is a descent group of Ξ‎∞ and (Ξ‎∞) is congruent to (Ξ‎∞). Ξ‎Γ‎ and Ξ‎ can be viewed as metric spaces. The chapter first considers the assumptions that Π‎ is an irreducible affine Coxeter diagram, Ξ‎ is a thick building of type Ξ‎, Γ‎is a finite descent group of Ξ‎, and Tits index �� = (Π‎, Θ‎, A). It then describes apartments that are endowed with reflection hyperplanes and reflection half-spaces before concluding with a theorem about a canonical isomorphism from the fixed point building Ξ‎Γ‎ to (Ξ‎Γ‎).
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Goebel, Kazimierz, and Stanislaw Prus. Elements of Geometry of Balls in Banach Spaces. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827351.001.0001.

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One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects contains: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory, and others. The aim of this book is to present basic facts from this field. It is addressed to advanced undergraduate and graduate students interested in the subject. For some it may result in further interest, a continuation and deepening of their study of the subject. It may be also useful for instructors running courses on functional analysis, supervising diploma theses or essays on various levels.
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Farb, Benson, and Dan Margalit. Thurston's Proof. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0016.

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This chapter describes Thurston's original path of discovery to the Nielsen–Thurston classification theorem. It first provides an example that illustrates much of the general theory, focusing on Thurston's iteration of homeomorphisms on simple closed curves as well as the linear algebra of train tracks. It then explains how the general theory works and presents Thurston's original proof of the Nielsen–Thurston classification. In particular, it considers the Teichmüller space and the measured foliation space. The chapter also discusses measured foliations on a pair of pants, global coordinates for measured foliation space, the Brouwer fixed point theorem, the Thurston compactification for the torus, and Markov partitions. Finally, it evaluates other approaches to proving the Nielsen–Thurston classification, including the use of geodesic laminations.
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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Unramified Galois Involutions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0032.

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This chapter describes the fixed point building of an automorphism of a Bruhat-Tits building Ξ‎ which induces an unramified Galois involution on the building at infinity Ξ‎∞. An element of G (for example, a Galois involution of Δ‎) is unramified if the subgroup of G it generates is unramified. Before presenting the main result, the chapter presents the notation stating that Δ‎ = Ξ‎∞ is the building at infinity of Ξ‎ with respect to its complete system of apartments and G = Aut(Δ‎), followed by definitions. The central theorem shows how an unramified Galois involution of Δ‎ is obtained. Here Γ‎ := τ‎ is a descent group of both Δ‎ and Ξ‎, there is a canonical isomorphism from Δ‎Γ‎ to (Ξ‎Γ‎), where Ξ‎Γ‎ and Ξ‎Γ‎ are the fixed point buildings.
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Tu, Loring W. Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.001.0001.

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Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah–Bott and Berline–Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, the book begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
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Burda, Zdzislaw, and Jerzy Jurkiewicz. Phase transitions. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.14.

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This article considers phase transitions in matrix models that are invariant under a symmetry group as well as those that occur in some matrix ensembles with preferred basis, like the Anderson transition. It first reviews the results for the simplest model with a nontrivial set of phases, the one-matrix Hermitian model with polynomial potential. It then presents a view of the several solutions of the saddle point equation. It also describes circular models and their Cayley transform to Hermitian models, along with fixed trace models. A brief overview of models with normal, chiral, Wishart, and rectangular matrices is provided. The article concludes with a discussion of the curious single-ring theorem, the successful use of multi-matrix models in describing phase transitions of classical statistical models on fluctuating two-dimensional surfaces, and the delocalization transition for the Anderson, Hatano-Nelson, and Euclidean random matrix models.
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Book chapters on the topic "Banach's fixed point theorem"

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Amster, Pablo. "The Banach Fixed Point Theorem." In Universitext, 29–51. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4614-8893-4_2.

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Siddiqi, Abul Hasan. "Banach Contraction Fixed Point Theorem." In Functional Analysis and Applications, 1–14. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-3725-2_1.

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Zeidler, Eberhard. "The Banach Fixed-Point Theorem and Iterative Methods." In Nonlinear Functional Analysis and its Applications, 15–48. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4838-5_2.

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Jost, Jürgen. "The Banach Fixed Point Theorem. The Concept of Banach Space." In Universitext, 43–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05306-5_5.

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Jost, Jürgen. "The Banach Fixed Point Theorem. The Concept of Banach Space." In Universitext, 41–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03635-8_5.

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Shen, A., and N. Vereshchagin. "Fixed point theorem." In The Student Mathematical Library, 41–53. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/stml/019/05.

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Zeidler, Eberhard. "Banach Spaces and Fixed-Point Theorems." In Applied Functional Analysis, 1–99. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0815-0_1.

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Latif, Abdul. "Banach Contraction Principle and Its Generalizations." In Topics in Fixed Point Theory, 33–64. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01586-6_2.

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Agarwal, Ravi P., Donal O’Regan, and D. R. Sahu. "Existence Theorems in Banach Spaces." In Fixed Point Theory for Lipschitzian-type Mappings with Applications, 211–78. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-75818-3_5.

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Agarwal, Praveen, Mohamed Jleli, and Bessem Samet. "Banach Contraction Principle and Applications." In Fixed Point Theory in Metric Spaces, 1–23. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2913-5_1.

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Conference papers on the topic "Banach's fixed point theorem"

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Daskalakis, Constantinos, Christos Tzamos, and Manolis Zampetakis. "A converse to Banach's fixed point theorem and its CLS-completeness." In STOC '18: Symposium on Theory of Computing. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3188745.3188968.

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Rodriguez, Virgilio, Rudolf Mathar, and Anke Schmeink. "Generalised Multi-Receiver Radio Network: Capacity and Asymptotic Stability of Power Control through Banach's Fixed-Point Theorem." In 2009 IEEE Wireless Communications and Networking Conference. IEEE, 2009. http://dx.doi.org/10.1109/wcnc.2009.4917736.

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Sahiner, Ahmet, and Tuba Yigit. "2–Cone Banach spaces and fixed point theorem." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756305.

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Auwalu, Abba, and Ali Denker. "Chatterjea-type fixed point theorem on cone rectangular metric spaces with banach algebras." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040595.

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Kopecká, Eva, and Simeon Reich. "Nonexpansive retracts in Banach spaces." In Fixed Point Theory and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc77-0-12.

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Grąziewicz, W. "Remarks on a boundary value problem in Banach spaces on the half-line." In Fixed Point Theory and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc77-0-9.

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"APPLICATION OF THE BANACH FIXED POINT THEOREM ON FUZZY QUASI-METRIC SPACES TO STUDY THE COST OF ALGORITHMS WITH TWO RECURRENCE EQUATIONS." In International Conference on Fuzzy Computation. SciTePress - Science and and Technology Publications, 2010. http://dx.doi.org/10.5220/0003081301050109.

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Stankovic´, Nikola, Sorin Olaru, and Silviu-Iulian Niculescu. "Further Remarks on Invariance Properties of Time-Delay Systems." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48234.

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For various problems of practical importance, such as disturbance rejection or constrained control, the determination of invariant sets provides insightful information on the influence of unknown bounded signals on the dynamical system behavior. In order to characterize the effect of those signals on the system, the determination of the minimal robust positively invariant (mRPI) set is of great interest. On the other side, the presence of time delays is ubiquitous in process control and it seems natural to use invariant set theory to analyze time delay systems affected by additive disturbance. The present paper deals with computation and characterization of the delay-independent minimal robust positively invariant region in the set-theoretic framework. The Banach fixed point theorem will be used to specify the existence and uniqueness conditions for this set. Here we also provide a procedure for the construction of invariant approximations of this limit set as well as discussion on the efficient computation for practical usage. Supplementary, at the end is pointed out an interesting correlation between proposed results and existence of the mRPI sets for switching dynamics. In this study we are particularly interested in discrete time systems. Outlined results are confirmed by a numerical example.
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Karapinar, Erdal. "Some fixed point theorems on the cone Banach spaces." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_0080.

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Banakh, Taras, and Robert Cauty. "A homological selection theorem implying a division theorem for Q-manifolds." In Fixed Point Theory and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc77-0-1.

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Reports on the topic "Banach's fixed point theorem"

1

Wos, L., and W. McCune. Searching for fixed point combinators by using automated theorem proving: A preliminary report. Office of Scientific and Technical Information (OSTI), September 1988. http://dx.doi.org/10.2172/6852789.

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