Fixed Point Theory and Variational Principles in Metric Spaces

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.

• Dedicated coverage of fixed point principles, variational principles, and equilibrium problems in metric spaces
• New and old results in metric fixed point theory for thorough understanding of concepts
• Examples and exercises for strengthening grasp on fundamentals
• Appendices on 'Some Basic Concepts and Inequalities' and 'Partial Ordering' for easy reference