Fixed Point Theory and Variational Principles in Metric Spaces

"The fixed-point theory in metric spaces came into the existence through the PhD work of Polish mathematician Stefan Banach in 1920. The outcome of the Banach contraction principle became the initial source of the theory. It evolved with time and is now important not only for nonlinear analysis but also for many other branches of mathematics. It has also been applied to sciences and engineering. Many extensions and generalizations of the Banach contraction principle are explored by mathematicians. The proposed book covers some of the main extensions and generalizations of the principle. It focuses on the basic techniques and results of topics like set-valued analysis, variational principles, and equilibrium problems. This book will be useful for researchers working in nonlinear analysis and optimization and can be a reference book for graduate and undergraduate students. There are some excellent books available on metric fixed point theory, but the above-mentioned topics are not covered in any single resource. The book includes a brief introduction to set-valued analysis with a focus on continuity and the fixed-point theory of set-valued maps and the last part of the book focuses on the application of fixed point theory"--

Preface; Acknowledgements; Notations and Abbreviations; 1. Basic Definitions and Concepts from Metric Spaces; 2. Fixed Point Theory in Metric Spaces; 3. Set-valued Analysis: Continuity and Fixed Point Theory; 4. Variational Principles and their Applications; 5. Equilibrium Problems and Extended Ekeland's Variational Principle; 6. Some Applications of Fixed Point Theory; Appendix A. Some Basic Concepts and Inequalities; Appendix B. Partial Ordering; References; Index.