Fixed Point Theory and Variational Principles in Metric Spaces

Qamrul Hasan Ansari; Daya Ram Sahu

doi:10.1017/9781009351430

The book is designed for undergraduates, graduates, and researchers of mathematics studying fixed point theory or nonlinear analysis. It deals with the fixed point theory for not only single-valued maps but also set-valued maps. The text is divided into three parts: fixed point theory for single-valued mappings, continuity and fixed point aspects of set-valued analysis, and variational principles and their equilibrium problems. It comprises a comprehensive study of these topics and includes all important results derived from them. The applications of fixed point principles and variational principles, and their generalizations to differential equations and optimization are covered in the text. An elementary treatment of the theory of equilibrium problems and equilibrium version of Ekeland's variational principle is also provided. New topics such as equilibrium problems, variational principles, Caristi's fixed point theorem, and Takahashi's minimization theorem with their applications are also included.

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Fixed Point Theory and Variational Principles in Metric Spaces

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-viii

Preface
pp ix-x

Acknowledgments
pp xi-xii

Notations and Abbreviations
pp xiii-xiv

1 - Basic Definitions and Concepts from Metric Spaces
pp 1-20

2 - Fixed Point Theory in Metric Spaces
pp 21-54

3 - Set-valued Analysis: Continuity and Fixed Point Theory
pp 55-102

4 - Variational Principles and Their Applications
pp 103-132

5 - Equilibrium Problems and Extended Ekeland’s Variational Principle
pp 133-168

6 - Some Applications of Fixed Point Theory
pp 169-200

Appendix A - Some Basic Concepts and Inequalities
pp 201-204

Appendix B - Partial Ordering
pp 205-206

References
pp 207-216

Index
pp 217-219

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Fixed Point Theory and Variational Principles in Metric Spaces

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