Fixed Point Theory and Variational Principles in Metric Spaces

Qamrul Hasan Ansari

ISBN 10: 1009351451 / ISBN 13: 9781009351454

Verlag: Cambridge University Press Nov 2023, 2023

Beschreibung

Neuware - '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'--.

Bestandsnummer des Verkäufers 9781009351454

Bibliografische Details

• Titel: Fixed Point Theory and Variational Principles in Metric Spaces
• Verlag: Cambridge University Press Nov 2023
• Erscheinungsjahr: 2023
• Sprache: Englisch
• ISBN-10: 1009351451
• ISBN-13: 9781009351454
• Einband: Buch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.