Fixed Point Theory and Variational Principles in Metric Spaces
Seiten
2023
Cambridge University Press (Verlag)
978-1-009-35145-4 (ISBN)
Cambridge University Press (Verlag)
978-1-009-35145-4 (ISBN)
The book is designed for undergraduates, graduates, and researchers of mathematics studying fixed point theory or nonlinear analysis. Basic techniques and results of topics such as fixed point theory, set-valued analysis, variational principles, and equilibrium problems are presented in an understandable and thorough manner.
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.
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.
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.
| Erscheinungsdatum | 23.11.2022 |
|---|---|
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 191 x 248 mm |
| Gewicht | 540 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-009-35145-1 / 1009351451 |
| ISBN-13 | 978-1-009-35145-4 / 9781009351454 |
| Zustand | Neuware |
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