Название: Recent Advances and Applications of Fuzzy Metric Fixed Point Theory
Автор: Dhananjay Gopal, Juan Martinez Moreno
Издательство: CRC Press
Год: 2024
Страниц: 215
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This book not only presents essential material to understand fuzzy metric fixed point theory, but also enables the readers to appreciate the recent advancements made in this direction. It contains seven chapters on different topics in fuzzy metric fixed point theory. These chapters cover a good range of interesting topics such as con- vergence problems in fuzzy metrics, fixed figure problems, and applications of fuzzy metrics.

The main focus is to unpack a number of diverse aspects of fuzzy metric fixed point theory and its applications in an understandable way so that it could help and motivate young graduates to explore new avenues of research to extend this flourishing area in different directions. The discussion on fixed figure problems and fuzzy contractive fixed point theorems and their different generalizations invites active researchers in this field to develop a new branch of fixed point theory.

Features:

Explore the latest research and developments in fuzzy metric fixed point theory.
Describes applications of fuzzy metrics to colour image processing.
Covers new topics on fuzzy fixed figure problems.
Filled with examples and open problems.

This book contains seven chapters with numerous illustrative examples, remarks, and some open problems concerning the related topics. This book is organized as follows:
Chapter 1 provides some fundamental concepts, definitions, and results on fuzzy sets and corresponding set theoretical operations, which are necessary for understanding the main topics such as fuzzy metrics and related theorems, propositions, and other ideas discussed in the remaining chapters.
Chapter 2 introduces the motivation of fuzzy distances and some basic results of fuzzy metrics. Several examples and counter examples are given to distinguish various classes of fuzzy metric spaces including open problems.
Chapter 3 deals with the problem of convergence and completeness of fuzzy metric spaces. Comparative diagrams are presented to simplify various types of convergence inclusion aspects.
Chapter 4 presents a concise study of fixed point problems concerning various classes of fuzzy contractive mappings including characterization of complete fuzzy metric spaces. We hope that the results presented in this chapter illustrate the direction of research over the last five decades up to the most recent contributions on the topic.
Chapter 5 studies some common fixed point results.
Chapter 6 presents most recent findings on the problem of fixed figure in the setting of GV-fuzzy metric spaces. The first section of this chapter deals with fixed circle concept. Other sections studies Cassini curves and fuzzy quasi non-expansive mappings.
Chapter 7 is devoted to study and explore various applications of fuzzy metric and corresponding fixed point results in image processing, integral and functional equations problems.

This book serves as a reference book for scientific investigators who want to analyze a simple and direct presentation of the fundamentals of the theory of fuzzy metric fixed point and its applications. It may also be used as a textbook for postgraduate and research students who try to derive future research scope in this area.