An in-depth guide to fixed-point theorems

✍ Scribed by (Mathematics) Rajinder Sharma (editor)

• Publisher: Nova Science Publishers Inc
• Year: 2021
• Tongue: English
• Leaves: 268
• Series: Mathematics research developments
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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
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