Fixed Point Theory

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Mohamed A Khamsi - One of the best experts on this subject based on the ideXlab platform.

  • Recent contributions to Fixed Point Theory of monotone mappings
    Journal of Fixed Point Theory and Applications, 2016
    Co-Authors: M. Bachar, Mohamed A Khamsi
    Abstract:

    In this manuscript, we discuss the latest Fixed Point results of monotone mappings. The Fixed Point Theory of such mappings has seen a tremendous interest in the last decade since the publication of Ran and Reurings paper in 2004. Fixed Point Theory for monotone mappings is useful and has many applications. For example when one is looking for a positive or negative solution, the use of the classical Fixed Point results is not adapted in this situation.

  • Fixed Point Theory in Metric Spaces: An Introduction
    Fixed Point Theory in Modular Function Spaces, 2015
    Co-Authors: Mohamed A Khamsi, W. M. Kozlowski
    Abstract:

    This chapter introduces the general concepts and results of the metric Fixed Point Theory. It sets the foundation for the coming chapters.

  • Fixed Point Theory in modular function spaces
    2015
    Co-Authors: Mohamed A Khamsi, W. M. Kozlowski, Simeon Reich
    Abstract:

    Introduction.- Fixed Point Theory in Metric Spaces: An Introduction.- Modular Function Spaces.- Geometry of Modular Function Spaces.- Fixed Point Existence Theorems in Modular Function Spaces.- Fixed Point Construction Processes.- Semigroups of Nonlinear Mappings in Modular Function Spaces.- Modular Metric Spaces.

  • Fixed Point Theory in Modular Function Spaces
    2015
    Co-Authors: Mohamed A Khamsi, Wojciech M. Kozlowski
    Abstract:

    This monograph provides a concise introduction to the main results and methods of the Fixed Point Theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and Fixed Point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the Theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions are suggested when applicable.   The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in Fixed Point Theory of mappings acting in modular function spaces

  • topics in Fixed Point Theory
    2014
    Co-Authors: Saleh A Almezel, Qamrul Hasan Ansari, Mohamed A Khamsi
    Abstract:

    1 Introduction to Metric Fixed Point Theory. M.A. Khamsi.- 2 Banach Contraction Principle and its Generalizations. Abdul Latif.- 3 Ekeland's Variational Principle and Its Extensions with Applications. Qamrul Hasan Ansari.- 4 Fixed Point Theory in Hyperconvex Metric Spaces. Rafael Espinola and Aurora Fernandez-Leon.- 5 An Introduction to Fixed Point Theory in Modular Function Spaces. W. M. Kozlowski.- 6 Fixed Point Theory in Ordered Sets from the Metric Point of View. M. Z. Abu-Sbeih and M. A. Khamsi.- 7 Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps. Hichem Ben-El-Mechaiekh.- 8 Some Iterative Methods for Fixed Point Problems. Q. H. Ansari and D. R. Sahu.- Index.

William A. Kirk - One of the best experts on this subject based on the ideXlab platform.

  • Metric Fixed Point Theory: a brief retrospective
    Fixed Point Theory and Applications, 2015
    Co-Authors: William A. Kirk
    Abstract:

    These remarks are based on a talk the writer gave at the 11th International Conference in Fixed Point Theory and Applications, held at Galatasaray University in Istanbul, Turkey, July 20-24, 2015. They represent selected thoughts on a career in research, largely devoted to metric Fixed Point Theory, that has spanned over 50 years.

  • Some problems in metric Fixed Point Theory
    Journal of Fixed Point Theory and Applications, 2008
    Co-Authors: Kazimierz Goebel, William A. Kirk
    Abstract:

    Three papers, published coincidentally and independently by Felix Browder, Dietrich Gohde, and W. A. Kirk in 1965, triggered a branch of mathematical research now called metric Fixed Point Theory. This is a survey of some of the highlights of that Theory, with a special emphasis on some of the problems that remain open.

  • Some recent results in metric Fixed Point Theory
    Journal of Fixed Point Theory and Applications, 2007
    Co-Authors: William A. Kirk
    Abstract:

    This is a survey of recent results on best approximation and Fixed Point Theory in certain geodesic spaces. Some of these results are related to fundamental Fixed Point theorems in topology that have been known for many years. However the metric approach is emphasized here.

  • Transfinite methods in metric Fixed-Point Theory
    Abstract and Applied Analysis, 2003
    Co-Authors: William A. Kirk
    Abstract:

    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.

  • an introduction to metric spaces and Fixed Point Theory
    2001
    Co-Authors: Mohamed A Khamsi, William A. Kirk
    Abstract:

    Preface. METRIC SPACES. Introduction. Metric Spaces. Metric Contraction Principles. Hyperconvex Spaces. "Normal" Structures in Metric Spaces. BANACH SPACES. Banach Spaces: Introduction. Continuous Mappings in Banach Spaces. Metric Fixed Point Theory. Banach Space Ultrapowers. Appendix: Set Theory. Bibliography. Index.

Donal O'regan - One of the best experts on this subject based on the ideXlab platform.

Lech Gorniewicz - One of the best experts on this subject based on the ideXlab platform.

  • Recent results on the topological Fixed Point Theory of multivalued mappings: a survey
    Fixed Point Theory and Applications, 2015
    Co-Authors: Jan Andres, Lech Gorniewicz
    Abstract:

    In this survey, we present current results from the topological Fixed Point Theory of multivalued mappings which were obtained by ourselves in the last five years (see Andres and Górniewicz in Fixed Point Theory 12(2):255-264, 2011; Topol. Methods Nonlinear Anal. 40:337-358, 2012; Libertas Mathematica 33(1):69-78, 2013; Int. J. Bifurc. Chaos 24(11):1450148, 2014; J. Nonlinear Convex Anal. 16(6):1013-1023, 2015; Int. J. Bifurc. Chaos, 2015, to appear). Some abstract theorems are applied to differential inclusions and multivalued fractals. A part of the deterministic Theory is randomized, including the applications to random differential inclusions.

  • handbook of topological Fixed Point Theory
    2005
    Co-Authors: R F Brown, Massimo Furi, Lech Gorniewicz, B Jiang
    Abstract:

    Preface. I. Homological Methods in Fixed Point Theory. 1. Coincidence Theory. 2. On the Lefschetz Fixed Point theorem. 3. Linearizations for maps of nilmanifolds and solvmanifolds. 4. Homotopy minimal periods. 5. Perodic Points and braid Theory. 6. Fixed Point Theory of multivalued weighted maps. 7. Fixed Point Theory for homogeneous spaces - a brief survey. II. Equivariant Fixed Point Theory. 8. A note on equivariant Fixed Point Theory. 9. Equivariant degree. 10. Bifurcations of solutions of SO (2)-symmetric nonlinear problems with variational structure. III. Nielsen Theory. 11. Nielsen root Theory. 12. More about Nielsen theories and their applications. 13. Algebraic techniques for calculating the Nielsen number on hyperbolic surfaces. 14. Fibre techniques in Nielsen Theory calculations. 15. Wecken theorem for Fixed and periodic Points. 16. A primer of Nielsen Fixed Point Theory. 17. Nielsen Fixed Point Theory on surfaces. 18. Relative Nielsen Theory. IV. Applications. 19. Applicable Fixed Point principles. 20. The Fixed Point index of the Poincare translation. 21. On the existence of equilibria and Fixed Points of maps under constraints. 22. Topological Fixed Point Theory and nonlinear differential equations. 23. Fixed Point results based on the Wazeski method.

  • topological Fixed Point Theory of multivalued mappings
    1999
    Co-Authors: Lech Gorniewicz
    Abstract:

    BACKGROUND IN TOPOLOGY.- MULTIVALUED MAPPINGS.- APPROXIMATION METHODS IN Fixed Point Theory OF MULTIVALUED MAPPINGS.- HOMOLOGICAL METHODS IN Fixed Point Theory OF MULTIVALUED MAPPINGS.- CONSEQUENCES AND APPLICATIONS.- Fixed Point Theory APPROACH TO DIFFERENTIAL INCLUSIONS.- RECENT RESULTS.

  • Topological Fixed Point Theory of Multivalued Mappings
    1999
    Co-Authors: Lech Gorniewicz
    Abstract:

    This volume presents a broad introduction to the topological Fixed Point Theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic Theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the Fixed Point Theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the Fixed Point approach to the Theory of ordinary differential inclusions. The work emphasises the topological aspect of the Theory, and gives special attention to the Lefschetz and Nielsen Fixed Point Theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers and graduate students working in the area of Fixed Point Theory, topology, nonlinear functional analysis, differential inclusions, and applications such as game Theory and mathematical economics

  • Fixed Point Theory Approach To Differential Inclusions
    Topological Fixed Point Theory of Multivalued Mappings, 1
    Co-Authors: Lech Gorniewicz
    Abstract:

    The aim of this chapter is to give a systematic and unified account of topics in Fixed Point Theory methods of differential inclusions which lie on the border line between topology and ordinary differential equations.

Ravi P. Agarwal - One of the best experts on this subject based on the ideXlab platform.

  • Fixed Point Theory in Metric Type Spaces
    2016
    Co-Authors: Ravi P. Agarwal, Donal O'regan, Erdal Karapınar, Antonio Francisco Roldán López De Hierro
    Abstract:

    Introduction with a Brief Historical Survey.- Preliminaries.- G-Metric Spaces.- Basic Fixed Point Results in the Setting of G-Metric Spaces.- Fixed Point Theorems in Partially Ordered G-Metric Spaces.- Further Fixed Point Results on G-Metric Spaces.- Fixed Point Theorems via Admissible Mappings.- New Approaches to Fixed Point Results on G-Metric Spaces.- Expansive Mappings.- Reconstruction of G-Metrics: G*-Metrics.- Multidimensional Fixed Point Theorems on G-Metric Spaces.- Recent Motivating Fixed Point Theory.

  • Fixed Point Theory for Cyclic Weak Kannan Type Mappings
    Journal of the Indian Mathematical Society, 2015
    Co-Authors: Ravi P. Agarwal, Donal O'regan, Maryam A Alghamdi, Naseer Shahzad
    Abstract:

    In this paper, we present Fixed Point Theory for weakly Kannan mappings that satisfy cyclical conditions on complete metric spaces.

  • Recent Motivating Fixed Point Theory
    Fixed Point Theory in Metric Type Spaces, 2015
    Co-Authors: Ravi P. Agarwal, Donal O'regan, Erdal Karapınar, Antonio Francisco Roldán-lópez-de-hierro
    Abstract:

    In this chapter, we present some recent Fixed/coincidence Point results. They show some current research, thoughts and directions on Fixed Point Theory in metric type spaces. However, in order not to enlarge the present book we will not include their proofs. We give the references so that the interested reader can find the proofs.

  • Fixed Point Theory for Admissible Type Maps with Applications
    Fixed Point Theory and Applications, 2009
    Co-Authors: Ravi P. Agarwal, Donal O'regan
    Abstract:

    We present new Leray-Schauder alternatives, Krasnoselskii and Lefschetz Fixed Point Theory for multivalued maps between Frechet spaces. As an application we show that our results are directly applicable to establish the existence of integral equations over infinite intervals.

  • Fixed Point Theory for compact absorbing contractive admissible type maps
    Applicable Analysis, 2008
    Co-Authors: Ravi P. Agarwal, Donal O'regan
    Abstract:

    In this article we present new Lefschetz Fixed Point theorems for compact absorbing contractive admissible maps between Frechet spaces. Also, we discuss condensing maps with a compact attractor. Finally we present new antipodal Fixed Point Theory for Kakutani maps.

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