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Fixed Point Theory and Graph Theory

Monther Rashid Alfuraidan and Qamrul Hasan Ansari, editors
Publisher: 
Academic Press
Publication Date: 
2016
Number of Pages: 
423
Format: 
Hardcover
Price: 
99.95
ISBN: 
9780128042953
Category: 
Proceedings
We do not plan to review this book.
  • Foreword
  • Acknowledgments
  • Preface
  • About the Authors
  • Chapter 1: Caristi-Browder Operator Theory in Distance Spaces
    • Abstract
    • 1.1 From the Caristi Fixed Point Theorems to Caristi, Caristi-Kirk and Caristi-Browder Operators
    • 1.2 List of Notations
    • 1.3 Weakly Picard Operators on L-Spaces
    • 1.4 Caristi-Browder Operators on Metric Spaces
    • 1.5 Caristi-Browder Operators on img + m -Metric Spaces
    • 1.6 Caristi-Browder Operators on s(img +)-Metric Spaces
    • 1.7 Caristi-Browder Operators on Kasahara Spaces
    • 1.8 Research Directions in the Caristi-Browder Operator Theory
  • Chapter 2: Iterative Approximation of Fixed Points of Single-valued Almost Contractions
    • Abstract
    • 2.1 Introduction
    • 2.2 Fixed Point Theorems for Single-valued Self Almost Contractions
    • 2.3 Implicit Almost Contractions
    • 2.4 Common Fixed Point Theorems for Almost Contractions
    • 2.5 Almost Contractive type Mappings on Product Spaces
    • 2.6 Fixed Point Theorems for Single-valued Nonself Almost Contractions
  • Chapter 3: Approximate Fixed Points
    • Abstract
    • 3.1 Introduction
    • 3.2 Approximate Fixed Points of Mappings in Banach Spaces
    • 3.3 Approximate Fixed Points of Mappings in Hyperbolic Spaces
    • 3.4 Approximate Fixed Points of Monotone Mappings
    • 3.5 Approximate Fixed Points of Nonlinear Semigroups
    • 3.6 Approximate Fixed Points of Monotone Nonlinear Semigroups
  • Chapter 4: Viscosity Methods for Some Applied Nonlinear Analysis Problems
    • Abstract
    • 4.1 Introduction
    • 4.2 Viscosity Method for Fixed Point Problems
    • 4.3 Viscosity Method for Split Common Fixed Point Problems
    • 4.4 Viscosity Method for Split Equilibrium Problems
  • Chapter 5: Extragradient Methods for Some Nonlinear Problems
    • Abstract
    • 5.1 Introduction
    • 5.2 Preliminaries
    • 5.3 Projection Gradient Method
    • 5.4 Extragradient Method for Nonexpansive Mappings and Variational Inequalities
    • 5.5 Modified Extragradient Method for Nonexpansive Mappings and Variational Inequalities
    • 5.6 Extragradient Method for Hierarchical Variational Inequalities
    • 5.7 Extragradient Methods for Split Feasibility Problems
    • Acknowledgments
  • Chapter 6: Iterative Methods for Nonexpansive Type Mappings
    • Abstract
    • 6.1 Introduction and Preliminaries
    • 6.2 Nonexpansive Mappings in Uniformly Convex Banach Spaces
    • 6.3 Nonexpansive Mappings in CAT(0) Spaces
    • 6.4 An Algorithm of Asymptotically Nonexpansive Mappings
    • 6.5 Existence and Approximation of Fixed Points
    • 6.6 Viscosity Method for Generalized Asymptotically Nonexpansive Mappings
    • Acknowledgments
  • Chapter 7: Metric Fixed Point Theory in Spaces with a Graph
    • Abstract
    • 7.1 Introduction
    • 7.2 Banach Contraction Principle
    • 7.3 Basic Definitions and Properties
    • 7.4 Banach Contraction Principle in Metric Spaces with a Graph
    • 7.5 Caristi’s Fixed Point Theorem
    • 7.6 The Contraction Principle in Modular Metric Spaces with a Graph
    • 7.7 Monotone Pointwise Contractions in Banach Spaces with a Graph
    • 7.8 Monotone Ćirić Quasi-Contraction Mappings
    • 7.9 Monotone Nonexpansive Mappings in Banach Spaces with a Graph
    • 7.10 Monotone Nonexpansive Mappings in Hyperbolic Metric Spaces with a Graph
    • 7.11 The Contraction Principle for Monotone Multivalued Mappings
    • 7.12 Monotone Nonexpansive Multivalued Mappings
    • Acknowledgments
  • Chapter 8: The Use of Retractions in the Fixed Point Theory for Ordered Sets
    • Abstract
    • 8.1 Introduction
    • 8.2 Chain-Complete Ordered Sets
    • 8.3 The Abian-Brown Theorem
    • 8.4 Comparative Retractions
    • 8.5 Irreducible Points
    • 8.6 Constraint Propagation
    • 8.7 Retractable Points
    • 8.8 Verifying Connected Collapsibility Directly
    • 8.9 Graphs
    • 8.10 Simplicial Complexes
    • 8.11 Topological Realizations
    • 8.12 Iterated Clique Graphs
    • 8.13 K-Null Comparability Graphs
    • Acknowledgments
  • Index