An in-depth guide to fixed-point theorems

Description

This book details fixed point theory, a gripping and wide-ranging field with applications in multifold areas of pure and applied mathematics. The content comprises both theoretical and practical applications. The evolution of the main theorems on the existence and uniqueness of fixed points of maps are presented. Applications covering topological properties, a nonlinear stochastic integral equation of the Hammerstein type, the existence and uniqueness of a common solution of the system of Urysohn integral equations, and the existence of a unique solution for linear equations system are included in this selection. Since the included chapters range from broad elucidations to functional research papers, the book provides readers with a satisfying analysis of the subject as well as a more comprehensive look at some functional recent advances. AN IN-DEPTH GUIDETO FIXED-POINT THEOREMS AN IN-DEPTH GUIDETO FIXED-POINT THEOREMS CONTENTS PREFACE ACKNOWLEDGMENTS Chapter 1TOPOLOGICAL PROPERTIES OFTVS-METRIC CONE SPACES ANDAPPLICATIONS TO FIXED POINT THEORY Abstract 1. INTRODUCTION 2. ORDERINGS 3. ORDERED TOPOLOGICAL VECTOR SPACES 4. CONE METRIC SPACES 5. APPLICATIONS TO APPROXIMATEAND FIXED POINTS 6. CARISTI AND RELATED FIXED POINT RESULTS ACKNOWLEDGMENTS REFERENCES Chapter 2FIXED POINTS OF SOME MIXED ITERATEDFUNCTION SYSTEMS Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULTS REFERENCES Chapter 3RANDOM ITERATION SCHEME LEADINGTO A RANDOM FIXED POINT THEOREMAND ITS APPLICATION Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. CONVERGENCE OF A RANDOM ITERATIONSCHEME (XU-MANN ITERATION) TO A RANDOMFIXED POINT 4. APPLICATION TO A RANDOM NONLINEAR INTEGRALEQUATION 5. WELL-POSEDNESS (ALMOST SURELY) OFA RANDOM FIXED POINT PROBLEM 5.1. The Multi Valued Deterministic Case 5.2. The Multi Valued Random Case ACKNOWLEDGMENT REFERENCES Chapter 4SOME COMMON FIXED POINT THEOREMSFOR SELF-MAPPINGS SATISFYINGRATIONAL INEQUALITIES CONTRACTIONIN COMPLEX VALUED METRIC SPACESAND APPLICATIONS Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULTS 3.1. Common Fixed Point for Two Self-Mappings 3.2. Common Fixed Point for Four Self-Mappings 4. APPLICATIONS 4.1. Application to Urysohn Integral Equations 4.2. Application to Linear System ACKNOWLEDGMENTS REFERENCES Chapter 5 BEST PROXIMITY POINT THEOREMS USING SIMULATIONS FUNCTIONS Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULTS ACKNOWLEDGMENTS REFERENCES Chapter 6ON B - METRIC SPACESAND THEIR COMPLETION ABSTRACT 1. INTRODUCTION 2. B -METRIC SPACES 3. COMPLETION OF B-METRIC SPACES Proposition REFERENCES Chapter 7ON BANACH CONTRACTION PRINCIPLEIN GENERALIZED B-METRIC SPACES ABSTRACT 1. INTRODUCTION 2. MAIN RESULTS REFERENCES Chapter 8METRIC FIXED POINT THEORYIN CONTEXT OF CYCLIC CONTRACTIONS ABSTRACT INTRODUCTION 1. SINGLE VALUED CYCLIC FIXED POINT THEOREMS 2. MUTLI-VALUED CYCLIC FIXED POINT THEOREMS 3. CYCLIC BEST PROXIMITY POINT THEOREMS ACKNOWLEDGMENTS REFERENCES Chapter 9AN INVESTIGATION OF THE FIXED POINTANALYSIS AND PRACTICES Abstract 1. INTRODUCTION 2. PRELIMINARIES 2.1. Introduction to Functional Analysis 2.2. Linear Operators on Banach Spaces 2.3. Complete Metric Spaces Additional Resources 2.5. Fixed Points 3. C- ALGEBRA VALUED b-METRIC SPACE 4. MAIN RESULTS 4.1. Uniqueness of Fixed Point 5. SOLUTION OF DIFFERENTIAL EQUATIONS ANDINTEGRAL EQUATIONS USING FIXED POINTTHEORY 5.1. Lipschitz Mapping REFERENCES Additional Resources ABOUT THE EDITORS INDEX Blank Page