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Journal articles on the topic 'Singularities (Mathematics) Fixed point theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Temar, Bahia, Ouiza Saif, and Smaïl Djebali. "A system of nonlinear fractional BVPs with ϕ-Laplacian operators and nonlocal conditions." Proyecciones (Antofagasta) 40, no. 2 (April 2021): 447–79. http://dx.doi.org/10.22199/issn.0717-6279-2021-02-0027.

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This work investigates the existence of multiple positive solutions for a system of two nonlinear higher-order fractional differential equations with ϕ-Laplacian operators and nonlocal conditions. A degenerate nonlinearity which obeys some general growth conditions is considered. The singularities are dealt with by approximating the fixed point operator. New existence results are presented by using the fixed point index theory. Examples of applications illustrate the theoretical results.

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2

Tudorache, Alexandru, and Rodica Luca. "On a singular Riemann–Liouville fractional boundary value problem with parameters." Nonlinear Analysis: Modelling and Control 26, no. 1 (January 1, 2021): 151–68. http://dx.doi.org/10.15388/namc.2021.26.21414.

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We investigate the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a positive parameter subject to nonlocal boundary conditions, which contain fractional derivatives and Riemann–Stieltjes integrals. The nonlinearity of the equation is nonnegative, and it may have singularities at its variables. In the proof of the main results, we use the fixed point index theory and the principal characteristic value of an associated linear operator. A related semipositone problem is also studied by using the Guo–Krasnosel’skii fixed point theorem.

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3

FISCHER, P., and D. GILLIS. "PLANE MAPS, SINGULARITIES AND QUASI-FIXED POINTS." International Journal of Bifurcation and Chaos 16, no. 01 (January 2006): 179–83. http://dx.doi.org/10.1142/s0218127406014691.

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This work investigates maps T of the plane with points p ∈ ℝ2 where T is undefined. Through the study of certain families with a singularity at the origin two very different dynamics will be illustrated. The first example will show that a singularity has no apparent effect on forward mapping. In this example there exists also an attractive fixed point. The second example will illustrate a singularity that exhibits attracting fixed point-like behavior.

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4

O'Regan, Donal. "Fixed Point Theory of." Applicable Analysis 69, no. 1-2 (June 1998): 414–16. http://dx.doi.org/10.1080/00036819808840643.

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5

Brown, Robert F. "Book Review: Fixed point theory." Bulletin of the American Mathematical Society 41, no. 02 (January 20, 2004): 267–72. http://dx.doi.org/10.1090/s0273-0979-04-01008-0.

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6

Sonoda, H. "The operator algebra at the Gaussian fixed-point." International Journal of Modern Physics A 36, no. 16 (June 2, 2021): 2150106. http://dx.doi.org/10.1142/s0217751x21501062.

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We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in [Formula: see text] dimensions. This amounts to perturbative construction of the [Formula: see text] theory where the parameters of the theory are momentum-dependent sources. Using the exact renormalization group (ERG) formalism, we show how the scaling properties of the sources are given by the short-distance singularities of the multiple products.

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7

Ege, Ozgur, and Ismet Karaca. "Digital homotopy fixed point theory." Comptes Rendus Mathematique 353, no. 11 (November 2015): 1029–33. http://dx.doi.org/10.1016/j.crma.2015.07.006.

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8

Brown, Robert F. "Epsilon Nielsen fixed point theory." Fixed Point Theory and Applications 2006 (2006): 1–11. http://dx.doi.org/10.1155/fpta/2006/29470.

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9

Wong, Peter. "Fixed-point theory for homogeneous spaces." American Journal of Mathematics 120, no. 1 (1998): 23–42. http://dx.doi.org/10.1353/ajm.1998.0008.

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10

Isac, G. "Supernormal cones and fixed point theory." Rocky Mountain Journal of Mathematics 17, no. 2 (June 1987): 219–26. http://dx.doi.org/10.1216/rmj-1987-17-2-219.

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11

Manoharan, Palanivel. "Lefschetz fixed point theory on fibrations." manuscripta mathematica 125, no. 1 (October 31, 2007): 127–37. http://dx.doi.org/10.1007/s00229-007-0145-8.

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12

Păcurar, Mădălina, and Ioan A. Rus. "Fixed point theory for cyclic -contractions." Nonlinear Analysis: Theory, Methods & Applications 72, no. 3-4 (February 2010): 1181–87. http://dx.doi.org/10.1016/j.na.2009.08.002.

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13

Budzyńska, Monika. "An example in holomorphic fixed point theory." Proceedings of the American Mathematical Society 131, no. 9 (March 11, 2003): 2771–77. http://dx.doi.org/10.1090/s0002-9939-03-06982-x.

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14

WITTEN, EDWARD. "GAUGE THEORY AND WILD RAMIFICATION." Analysis and Applications 06, no. 04 (October 2008): 429–501. http://dx.doi.org/10.1142/s0219530508001195.

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The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities, Stokes phenomena, isomonodromic deformation, and, from a physical point of view, new surface operators associated with higher order singularities.

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15

Lau, AnthonyTo-Ming, and Tomonari Suzuki. "Takahashi's Legacy in Fixed Point Theory." Fixed Point Theory and Applications 2010, no. 1 (2010): 721648. http://dx.doi.org/10.1155/2010/721648.

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16

Xu, Hong-Kun. "Metric fixed point theory for multivalued mappings." Dissertationes Mathematicae 389 (2000): 1–39. http://dx.doi.org/10.4064/dm389-0-1.

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17

Chen, Chi-Ming, Tong-Huel Chang, and Chi-Lin Yen. "FIXED-POINT THEORY FOR k-SET CONTRACTION." Journal of the Korean Mathematical Society 41, no. 2 (March 1, 2004): 243–48. http://dx.doi.org/10.4134/jkms.2004.41.2.243.

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18

JERIBI, Aref, Bilel KRICHEN, and Bilel MEFTEH. "Fixed point theory in WC--Banach algebras." TURKISH JOURNAL OF MATHEMATICS 40 (2016): 283–91. http://dx.doi.org/10.3906/mat-1504-42.

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19

Kelly, Michael R. "Isotopic Homeomorphisms and Nielsen Fixed Point Theory." Rocky Mountain Journal of Mathematics 24, no. 2 (June 1994): 563–78. http://dx.doi.org/10.1216/rmjm/1181072419.

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20

GROOT NIBBELINK, STEFAN. "SHAPE OF GAUGE FIELD TADPOLES IN HETEROTIC STRING THEORY." Modern Physics Letters A 20, no. 03 (January 30, 2005): 155–68. http://dx.doi.org/10.1142/s0217732305016282.

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Orbifolds in field theory are potentially singular objects for at their fixed points the curvature becomes infinite, therefore one may wonder whether field theory calculations near orbifold singularities can be trusted. String theory is perfectly well defined on orbifolds and can therefore be taken as a UV completion of field theory on orbifolds. We investigate the properties of field and string theory near orbifold singularities by reviewing the computation of a one-loop gauge field tadpole. We find that in string theory the twisted states give contributions that have a spread of a couple of string lengths around the singularity, but otherwise the field theory picture is confirmed. One additional surprise is that in some orbifold models one can identify local tachyons that give contributions near the orbifold fixed point.

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21

Ma, Tiantian. "Positive Periodic Solution of Second-Order Coupled Systems with Singularities." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/504573.

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This paper establishes the existence of periodic solution for a kind of second-order singular nonautonomous coupled systems. Our approach is based on fixed point theorem in cones. Examples are given to illustrate the main result.

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22

Moeckel, Richard. "Generic bifurcations of the twist coefficient." Ergodic Theory and Dynamical Systems 10, no. 1 (March 1990): 185–95. http://dx.doi.org/10.1017/s0143385700005472.

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AbstractWe study the behavior of the twist coefficient near an elliptic fixed point for a one-parameter family of area-preserving diffeomorphisms. By looking at the singularities near resonance we can explain the sign changes which are typically found in such a family.

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23

Park, Sehie. "Recent results in analytical fixed point theory." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): 977–86. http://dx.doi.org/10.1016/j.na.2005.02.026.

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24

Agarwal, Ravi P., and Donal O'Regan. "Fixed Point Theory for k–CAR Sets." Journal of Mathematical Analysis and Applications 251, no. 1 (November 2000): 13–27. http://dx.doi.org/10.1006/jmaa.2000.7016.

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25

Kirk, W. A. "Transfinite methods in metric fixed-point theory." Abstract and Applied Analysis 2003, no. 5 (2003): 311–24. http://dx.doi.org/10.1155/s1085337503205029.

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This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.

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26

Abchouyeh, Maryam Aghaei, Behrouz Mirza, Parisa Shahidi, and Fatemeh Oboudiat. "Late time dynamics of f(R,T,RμνTμν) gravity." International Journal of Geometric Methods in Modern Physics 17, no. 01 (January 2020): 2050008. http://dx.doi.org/10.1142/s0219887820500085.

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Dynamical behavior and future singularities of [Formula: see text] gravitational theory are investigated. This gravitational model is a more complete form of the [Formula: see text] gravity which can offer new dynamics for the universe. We investigate this gravitational theory for the case [Formula: see text] using the method of autonomous dynamical systems and by assuming an interaction between matter and dark energy. The fixed points are identified and the results are consistent with standard cosmology and show that for small [Formula: see text], the radiation-dominated era is an unstable fixed point of the theory and the universe will continue its procedure toward matter era which is a saddle point of the theory and allows the evolution to dark energy-dominated universe. Finally, the dark energy-dominated epoch is a stable fixed point and will be the late time attractor for the universe. We also consider future singularities for the two [Formula: see text] and [Formula: see text] cases and for [Formula: see text] and [Formula: see text]. Our results show that for the case of [Formula: see text], the future singularities of the universe will happen in the same condition as do for the Einstein–Hilbert FRW universe. However, a new type of singularity is obtained for [Formula: see text] that is captured by [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text].

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27

MURESAN, ANTON S. "The theory of some asymptotic fixed point theorems." Carpathian Journal of Mathematics 30, no. 3 (2014): 361–68. http://dx.doi.org/10.37193/cjm.2014.03.07.

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In this paper we present the theory about some fixed point theorems for convex contraction mappings. We give some results on data dependence of fixed points, on sequences of operators and fixed points, on well-possedness of fixed point problem, on limit shadowing property and on Ulam-Hyers stability for equations of fixed points.

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28

Smart, D. R. "Book Review: The theory of fixed point classes." Bulletin of the American Mathematical Society 23, no. 2 (October 1, 1990): 630–34. http://dx.doi.org/10.1090/s0273-0979-1990-16010-0.

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29

Barnes, Donald W., and Larry A. Lambe. "A fixed point approach to homological perturbation theory." Proceedings of the American Mathematical Society 112, no. 3 (March 1, 1991): 881. http://dx.doi.org/10.1090/s0002-9939-1991-1057939-0.

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30

Du, Dapeng. "An Alternative Way of Utilizing Fixed Point Theory." Chinese Annals of Mathematics, Series B 41, no. 6 (November 12, 2020): 861–72. http://dx.doi.org/10.1007/s11401-020-0237-2.

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31

Lowenthal, Franklin, Arnold Langsen, and Clark T. Benson. "Merton's Partial Differential Equation and Fixed Point Theory." American Mathematical Monthly 105, no. 5 (May 1998): 412. http://dx.doi.org/10.2307/3109802.

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32

Eplett, W. J. R. "A fixed point approach to local minimax theory." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 2 (March 1986): 339–46. http://dx.doi.org/10.1017/s0305004100064252.

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AbstractThe generalized Neyman-Pearson theorem for constructing robust hypothesis tests proved by Huber and Strassen is obtained here as an application of the Kakutani-Fan fixed point theorem. The same technique is applied to obtain the existence of locally minimax estimators.

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33

Lowenthal, Franklin, Arnold Langsen, and Clark T. Benson. "Merton's Partial Differential Equation and Fixed Point Theory." American Mathematical Monthly 105, no. 5 (May 1998): 412–20. http://dx.doi.org/10.1080/00029890.1998.12004903.

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34

Hussain, N., and A. R. Khan. "Common fixed-point results in best approximation theory." Applied Mathematics Letters 16, no. 4 (May 2003): 575–80. http://dx.doi.org/10.1016/s0893-9659(03)00039-9.

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35

Karapınar, Erdal. "Fixed point theory for cyclic weak ϕ-contraction." Applied Mathematics Letters 24, no. 6 (June 2011): 822–25. http://dx.doi.org/10.1016/j.aml.2010.12.016.

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36

Fora, A. A. "Fixed point theory and product, sub-, super-spaces." Periodica Mathematica Hungarica 16, no. 2 (June 1985): 97–113. http://dx.doi.org/10.1007/bf01857590.

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37

O’Regan, Donal. "Fixed point theory for permissible extension type maps." Rendiconti del Circolo Matematico di Palermo 58, no. 3 (December 2009): 477–84. http://dx.doi.org/10.1007/s12215-009-0037-8.

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38

BARAŃSKI, KRZYSZTOF. "Hausdorff dimension of hairs and ends for entire maps of finite order." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 3 (November 2008): 719–37. http://dx.doi.org/10.1017/s0305004108001515.

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AbstractWe study transcendental entire mapsfof finite order, such that all the singularities off−1are contained in a compact subset of the immediate basinBof an attracting fixed point off. Then the Julia set offconsists of disjoint curves tending to infinity (hairs), attached to the unique point accessible fromB(endpoint of the hair). We prove that the Hausdorff dimension of the set of endpoints of the hairs is equal to 2, while the union of the hairs without endpoints has Hausdorff dimension 1, which generalizes the result for exponential maps. Moreover, we show that for every transcendental entire map of finite order from class(i.e. with bounded set of singularities) the Hausdorff dimension of the Julia set is equal to 2.

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39

García-Falset, Jesús, Enrique Llorens-Fuster, and Elena Moreno-Gálvez. "Fixed point theory for multivalued generalized nonexpansive mappings." Applicable Analysis and Discrete Mathematics 6, no. 2 (2012): 265–86. http://dx.doi.org/10.2298/aadm120712017g.

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A very general class of multivalued generalized nonexpansive mappings is defined. We also give some fixed point results for these mappings, and finally we compare and separate this class from the other multivalued generalized nonexpansive mappings introduced in the recent literature.

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40

Annaby, M. H., Z. S. Mansour, and I. A. Soliman. "q-Titchmarsh-Weyl theory: series expansion." Nagoya Mathematical Journal 205 (March 2012): 67–118. http://dx.doi.org/10.1017/s002776300001045x.

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AbstractWe establish aq-Titchmarsh-Weyl theory for singularq-Sturm-Liouville problems. We defineq-limit-point andq-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jacksonq-Bessel functions is given. This example leads to the completeness of a wide class ofq-cylindrical functions.

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41

Kohlenbach, Ulrich. "Some computational aspects of metric fixed-point theory." Nonlinear Analysis: Theory, Methods & Applications 61, no. 5 (May 2005): 823–37. http://dx.doi.org/10.1016/j.na.2005.01.075.

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42

Ey, Kristine, and Christian Pötzsche. "Asymptotic behavior of recursions via fixed point theory." Journal of Mathematical Analysis and Applications 337, no. 2 (January 2008): 1125–41. http://dx.doi.org/10.1016/j.jmaa.2007.04.052.

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43

Park, Sehie. "A Unified Fixed Point Theory in Generalized Convex Spaces." Acta Mathematica Sinica, English Series 23, no. 8 (June 21, 2007): 1509–26. http://dx.doi.org/10.1007/s10114-007-0947-3.

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44

Baillon, Jean-Bernard, and Stephen Simons. "Almost-fixed-point and fixed-point theorems for discrete-valued maps." Journal of Combinatorial Theory, Series A 60, no. 1 (May 1992): 147–54. http://dx.doi.org/10.1016/0097-3165(92)90046-w.

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45

RUS, IOAN A., and MARCEL-ADRIAN SERBAN. "Basic problems of the metric fixed point theory and the relevance of a metric fixed point theorem." Carpathian Journal of Mathematics 29, no. 2 (2013): 239–58. http://dx.doi.org/10.37193/cjm.2013.02.04.

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In this paper we present some basic problems of the metric fixed point theory (existence, uniqueness, settheoretic aspects (Bessaga, Janos, Rus, ...), order-theoretic aspects (Ekeland, Bronsted, Caristi, Kirk, Jachymski, ...), convergence of the succesive approximations, data dependence (general estimation, Ulam problem, dependence on the parameters, ...), well-posedness of the fixed point problem, limit shadowing property, stability, Gronwall lemmas, comparison lemmas, retractibility, ...). Following [I. A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559] we define the relevance of a metrical fixed point theorem by the impact of the theorem on these basic problems. Some case studies are presented.

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46

Ben Amar, Afif, Mohamed Amine Cherif, and Maher Mnif. "Fixed-Point Theory on a Frechet Topological Vector Space." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–9. http://dx.doi.org/10.1155/2011/390720.

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We establish some versions of fixed-point theorem in a Frechet topological vector spaceE. The main result is that every mapA=BC(whereBis a continuous map andCis a continuous linear weakly compact operator) from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Krasnoselskii fixed-point theorem. Our first result extend the well-known Krasnoselskii's fixed-point theorem forU-contractions and weakly compact mappings, while the second one, by assuming that the family{T(⋅,y):y∈C(M)whereM⊂EandC:M→Ea compactoperator}is nonlinearφequicontractive, we give a fixed-point theorem for the operator of the formEx:=T(x,C(x)).

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47

MURESAN, VIORICA, and ANTON S. MURESAN. "On the theory of fixed point theorems for convex contraction mappings." Carpathian Journal of Mathematics 31, no. 3 (2015): 365–71. http://dx.doi.org/10.37193/cjm.2015.03.13.

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Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations.

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48

LEVY, ROBERT. "FIXED POINT THEORY AND STRUCTURAL OPTIMIZATION." Engineering Optimization 17, no. 4 (June 1991): 251–61. http://dx.doi.org/10.1080/03052159108941074.

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49

Reem, Daniel, Simeon Reich, and Alexander J. Zaslavski. "Two results in metric fixed point theory." Journal of Fixed Point Theory and Applications 1, no. 1 (January 13, 2007): 149–57. http://dx.doi.org/10.1007/s11784-006-0011-4.

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50

Goebel, Kazimierz, and W. A. Kirk. "Some problems in metric fixed point theory." Journal of Fixed Point Theory and Applications 4, no. 1 (October 2008): 13–25. http://dx.doi.org/10.1007/s11784-008-0076-3.

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