| Description |
1 online resource (xi, 304 pages) |
| Contents |
880-01 Introduction to Metric Fixed Point Theory / M.A. Khamsi -- Banach Contraction Principle and its Generalizations / Abdul Latif -- Ekeland's Variational Principle and Its Extensions with Applications / Qamrul Hasan Ansari -- Fixed Point Theory in Hyperconvex Metric Spaces / Rafael Espinola and Aurora Fernandez-Leon -- An Introduction to Fixed Point Theory in Modular Function Spaces / W.M. Kozlowski -- Fixed Point Theory in Ordered Sets from the Metric Point of View / M.Z. Abu-Sbeih and M.A. Khamsi -- Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps / Hichem Ben-El-Mechaiekh -- Some Iterative Methods for Fixed Point Problems / Q.H. Ansari and D.R. Sahu |
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880-01/(S Machine generated contents note: 1.1. Introduction / M.A. Khamsi -- 1.2. Metric Fixed Point Theory / M.A. Khamsi -- 1.3. Caristi-Ekeland Extension / M.A. Khamsi -- 1.4. Converse Problem / M.A. Khamsi -- 1.5. Some Applications / M.A. Khamsi -- 1.5.1. ODE and Integral Equations / M.A. Khamsi -- 1.5.2. Cantor and Fractal Sets / M.A. Khamsi -- 1.6. Historical Note / M.A. Khamsi -- 1.7. Metric Fixed Point Theory in Banach Spaces / M.A. Khamsi -- 1.7.1. Classical Existence Results / M.A. Khamsi -- 1.7.2. Normal Structure Property / M.A. Khamsi -- 1.7.3. More on Normal Structure Property / M.A. Khamsi -- 1.7.4. Normal Structure and Smoothness / M.A. Khamsi -- 1.7.5. Karlovitz-Goebel Lemma / M.A. Khamsi -- 1.8. Nonstandard Techniques / M.A. Khamsi -- 1.8.1. Extending Mappings to Ultrapowers / M.A. Khamsi -- 1.9. More on Metric Fixed Point Theory in Metric Spaces / M.A. Khamsi -- 1.9.1. Menger Convexity in Metric Spaces / M.A. Khamsi -- 1.9.2. Uniformly Convex Metric Spaces / M.A. Khamsi -- 1.9.3. Fixed Point Property in Uniformly Convex Metric Spaces / M.A. Khamsi -- 1.10. Convexity Structures / M.A. Khamsi -- 1.10.1. Hyperconvex Metric Spaces / M.A. Khamsi -- References / M.A. Khamsi -- 2.1. Introduction / Abdul Latif -- 2.2. Contractions: Definition and Examples / Abdul Latif -- 2.3. Banach Contraction Principle with Some Applications / Abdul Latif -- 2.4. Some Other Extensions of BCP for Single-Valued Mappings / Abdul Latif -- 2.5. Caristi's Fixed Point Theorem / Abdul Latif -- 2.6. Some Extensions of BCP Under Generalized Distances / Abdul Latif -- 2.7. Multivalued Versions of BCP / Abdul Latif -- References / Abdul Latif -- 3.1. Introduction / Qamrul Hasan Ansari -- 3.2. Ekeland's Variational Principle in Complete Metric Spaces / Qamrul Hasan Ansari -- 3.3. Applications to Fixed Point Theorems / Qamrul Hasan Ansari -- 3.4. Applications to Optimization / Qamrul Hasan Ansari -- 3.5. Applications to Weak Sharp Minima / Qamrul Hasan Ansari -- 3.6. Equilibrium Problems and Extended Ekeland's Variational Principle / Qamrul Hasan Ansari -- 3.6.1. Equilibrium Problems / Qamrul Hasan Ansari -- 3.6.2. Extended Ekeland's Variational Principle / Qamrul Hasan Ansari -- Appendix A / Qamrul Hasan Ansari -- References / Qamrul Hasan Ansari -- 4.1. Introduction and Basic Definitions / Rafael Espinola / Aurora Fernández-León -- 4.2. Some Basic Properties of Hyperconvex Metric Spaces / Rafael Espinola / Aurora Fernández-León -- 4.3. Hyperconvexity, Injectivity, and Retractions / Rafael Espinola / Aurora Fernández-León -- 4.4. Isbell's Hyperconvex Hull / Rafael Espinola / Aurora Fernández-León -- 4.5. Topological Fixed Point Property and Hyperconvexity / Rafael Espinola / Aurora Fernández-León -- 4.6. Metric Fixed Point Property and Hyperconvexity / Rafael Espinola / Aurora Fernández-León -- 4.7. Metric Fixed Point Property for Multivalued Mappings and Nonexpansive Selections / Rafael Espinola / Aurora Fernández-León -- 4.8. KKM Theory and Hyperconvex Spaces / Rafael Espinola / Aurora Fernández-León -- 4.9. Fixed Point Theory and R-Trees / Rafael Espinola / Aurora Fernández-León -- 4.10. New Trends in Hyperconvexity / Rafael Espinola / Aurora Fernández-León -- 4.10.1. Two Long-Standing Open Problems / Rafael Espinola / Aurora Fernández-León -- 4.10.2. Ultrametrics and Hyperconvex Metric Spaces / Rafael Espinola / Aurora Fernández-León -- 4.10.3. Diversities and Hyperconvexity / Rafael Espinola / Aurora Fernández-León -- 4.10.4. Q-hyperconvexity / Rafael Espinola / Aurora Fernández-León -- References / Rafael Espinola / Aurora Fernández-León -- 5.1. Introduction / W.M. Kozlowski -- 5.2. Modular Function Spaces and Modular Geometry / W.M. Kozlowski -- 5.2.1. Introduction to Modular Function Spaces / W.M. Kozlowski -- 5.2.2. Geometrical Properties of Modular Function Spaces / W.M. Kozlowski -- 5.2.3. Nonlinear Mappings in Modular Function Spaces / W.M. Kozlowski -- 5.3. Existence of Fixed Points / W.M. Kozlowski -- 5.3.1. Generalized Contractions in Modular Function Spaces / W.M. Kozlowski -- 5.3.2. Generalized Nonexpansive Mappings / W.M. Kozlowski -- 5.4. Convergence of Fixed Point Iterative Algorithms / W.M. Kozlowski -- 5.5. Semigroups of Mappings in Modular Function Spaces / W.M. Kozlowski -- References / W.M. Kozlowski -- 6.1. Introduction / M.A. Khamsi / M.Z. Abu-Sbeih -- 6.2. Generalized Metric Spaces / M.A. Khamsi / M.Z. Abu-Sbeih -- 6.3. Retraction Property / M.A. Khamsi / M.Z. Abu-Sbeih -- 6.4. Fixed Point Property / M.Z. Abu-Sbeih / M.A. Khamsi -- 6.5. Externally Complete Sets / M.A. Khamsi / M.Z. Abu-Sbeih -- References / M.Z. Abu-Sbeih / M.A. Khamsi -- 7.1. Introduction and Preliminaries / Hichem Ben-El-Mechaiekh -- 7.1.1. Elementary Proofs of the Brouwer and Schauder-Tychonoff Fixed Point Theorems / Hichem Ben-El-Mechaiekh -- 7.2. Ky Fan and Kakutani Maps / Hichem Ben-El-Mechaiekh -- 7.2.1. Ky Fan Maps / Hichem Ben-El-Mechaiekh -- 7.2.2. Kakutani Maps / Hichem Ben-El-Mechaiekh -- 7.3. Continuous Selections and Approximations / Hichem Ben-El-Mechaiekh -- 7.3.1. Continuous Selections for Ky Fan Maps / Hichem Ben-El-Mechaiekh -- 7.3.2. Continuous Approximations of Kakutani Maps / Hichem Ben-El-Mechaiekh -- 7.4. Browder-Ky Fan and the Kakutani-Ky Fan Fixed Point Theorems and Their Consequences / Hichem Ben-El-Mechaiekh -- 7.4.1. Browder-Ky Fan Fixed Point Theorem / Hichem Ben-El-Mechaiekh -- 7.4.2. Kakutani-Ky Fan Fixed Point Theorem / Hichem Ben-El-Mechaiekh -- 7.4.3. Coincidence Theorems / Hichem Ben-El-Mechaiekh -- 7.5. Relaxing Compactness and Related Results / Hichem Ben-El-Mechaiekh -- 7.5.1. Coercivity Condition (κ) / Hichem Ben-El-Mechaiekh -- 7.5.2. Intersection Theorems: KKM and Matching / Hichem Ben-El-Mechaiekh -- 7.5.3. Browder-Ky Fan Theorem on Star-Shaped Domains / Hichem Ben-El-Mechaiekh -- 7.5.4. Leray-Schauder Alternative for Kakutani Maps / Hichem Ben-El-Mechaiekh -- 7.6. Systems of Nonlinear Inequalities and Applications / Hichem Ben-El-Mechaiekh -- 7.7. Concluding Remarks / Hichem Ben-El-Mechaiekh -- References / Hichem Ben-El-Mechaiekh -- 8.1. Introduction / D.R. Sahu / Q.H. Ansari -- 8.2. Preliminaries / Q.H. Ansari / D.R. Sahu -- 8.2.1. LE Property and the AF Point Property for Nonlinear Operators / Q.H. Ansari / D.R. Sahu -- 8.2.2. Nearly Lipschitzian Mappings / Q.H. Ansari / D.R. Sahu -- 8.2.3. Asymptotically κ-strict Pseudocontractive Mappings in the Intermediate Sense / D.R. Sahu / Q.H. Ansari -- 8.3. Picard Iterative Method / Q.H. Ansari / D.R. Sahu -- 8.4. Mann Iterative Method / D.R. Sahu / Q.H. Ansari -- 8.5. Ishikawa Iterative Method / Q.H. Ansari / D.R. Sahu -- 8.6. Helpern Iterative Method / D.R. Sahu / Q.H. Ansari -- 8.7. CQ Iteration Method / Q.H. Ansari / D.R. Sahu -- 8.8. Browder Iterative Method / D.R. Sahu / Q.H. Ansari -- References / Q.H. Ansari / D.R. Sahu |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Online resource; title from PDF title page (SpringerLink, viewed October 28, 2013) |
| Subject |
Fixed point theory.
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Mathematics.
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Mathematics
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Mathematics
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Fixed point theory
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| Form |
Electronic book
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| Author |
Almezel, Saleh, editor
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Ansari, Qamrul Hasan, editor
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Khamsi, Mohamed A., editor
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| ISBN |
9783319015866 |
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3319015869 |
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