Format:
Online-Ressource (XI, 304 p, online resource)
ISBN:
9783319015866
Series Statement:
SpringerLink
Content:
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 Espínola and Aurora Fernández-León.- 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
Content:
The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle
Note:
Description based upon print version of record
,
Preface; Contents; Contributors; Chapter1 Introduction to Metric Fixed Point Theory; 1.1 Introduction; 1.2 Metric Fixed Point Theory; 1.3 Caristi-Ekeland Extension; 1.4 The Converse Problem; 1.5 Some Applications; 1.5.1 ODE and Integral Equations; 1.5.2 Cantor and Fractal Sets; 1.6 Historical Note; 1.7 Metric Fixed Point Theory in Banach Spaces; 1.7.1 Classical Existence Results; 1.7.2 The Normal Structure Property; 1.7.3 More on Normal Structure Property; 1.7.4 Normal Structure and Smoothness; 1.7.5 Karlovitz-Goebel Lemma; 1.8 Nonstandard Techniques; 1.8.1 Extending Mappings to Ultrapowers
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1.9 More on Metric Fixed Point Theory in Metric Spaces1.9.1 Menger Convexity in Metric Spaces; 1.9.2 Uniformly Convex Metric Spaces; 1.9.3 Fixed Point Property in Uniformly Convex Metric Spaces; 1.10 The Convexity Structures; 1.10.1 Hyperconvex Metric Spaces; References; Chapter2 Banach Contraction Principle and Its Generalizations; 2.1 Introduction; 2.2 Contractions: Definition and Examples; 2.3 The Banach Contraction Principle with Some Applications; 2.4 Some Other Extensions of BCP for Single-Valued Mappings; 2.5 Caristi's Fixed Point Theorem
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2.6 Some Extensions of BCP Under Generalized Distances2.7 Multivalued Versions of BCP; References; Chapter3 Ekeland's Variational Principle and Its Extensionswith Applications; 3.1 Introduction; 3.2 Ekeland's Variational Principle in Complete Metric Spaces; 3.3 Applications to Fixed Point Theorems; 3.4 Applications to Optimization; 3.5 Applications to Weak Sharp Minima; 3.6 Equilibrium Problems and Extended Ekeland's Variational Principle; 3.6.1 Equilibrium Problems; 3.6.2 Extended Ekeland's Variational Principle; Appendix A; References
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Chapter4 Fixed Point Theory in Hyperconvex Metric Spaces4.1 Introduction and Basic Definitions; 4.2 Some Basic Properties of Hyperconvex Metric Spaces; 4.3 Hyperconvexity, Injectivity, and Retractions; 4.4 Isbell's Hyperconvex Hull; 4.5 Topological Fixed Point Property and Hyperconvexity; 4.6 Metric Fixed Point Property and Hyperconvexity; 4.7 Metric Fixed Point Property for Multivalued Mappings and Nonexpansive Selections; 4.8 KKM Theory and Hyperconvex Spaces; 4.9 Fixed Point Theory and R-Trees; 4.10 New Trends in Hyperconvexity; 4.10.1 Two Long-Standing Open Problems
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4.10.2 Ultrametrics and Hyperconvex Metric Spaces4.10.3 Diversities and Hyperconvexity; 4.10.4 Q-hyperconvexity; References; Chapter5 An Introduction to Fixed Point Theory in Modular Function Spaces; 5.1 Introduction; 5.2 Modular Function Spaces and Modular Geometry; 5.2.1 Introduction to Modular Function Spaces; 5.2.2 Geometrical Properties of Modular Function Spaces; 5.2.3 Nonlinear Mappings in Modular Function Spaces; 5.3 Existence of Fixed Points; 5.3.1 Generalized Contractions in Modular Function Spaces; 5.3.2 Generalized Nonexpansive Mappings
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5.4 Convergence of Fixed Point Iterative Algorithms
Additional Edition:
ISBN 9783319015859
Additional Edition:
Erscheint auch als Druck-Ausgabe Topics in fixed point theory Cham : Springer, 2014 ISBN 9783319015859
Language:
English
Subjects:
Mathematics
Keywords:
Fixpunkttheorie
;
Fixpunkt
DOI:
10.1007/978-3-319-01586-6
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