1st Edition

# Recent Advances and Applications of Fuzzy Metric Fixed Point Theory

214 Pages 15 B/W Illustrations
by Chapman & Hall

214 Pages 15 B/W Illustrations
by Chapman & Hall

Also available as eBook on:

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 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.

1. Fuzzy Sets and Basic Operation. 1.1. Introduction. 1.2. Fuzzy Set. 1.3. Operations on Fuzzy Set. 1.4. References. 2. Origin and Motivation of Fuzzy Metric. 2.1.  Introduction. 2.2. KM-Fuzzy metric Space. 2.3.  GV-Fuzzy metric Space. 2.4. Some especial class of Fuzzy metric spaces. 2.5. References. 3. Convergence in Fuzzy Metric Spaces. 3.1. Introduction. 3.2. GV. 3.3. Convergence. 3.4. p-Convergence. 3.5. s-convergence. 3.6. Compactness and completeness. 3.7. Inclusion diagram. 3.8. References. 4. Theory of fuzzy contractive mappings and fixed points. 4.1. Introduction. 4.2. Fuzzy contractive mappings. 4.3. Caristi type mapping and fixed point. 4.4. References. 5. Common fixed-point theorems in fuzzy metric spaces. 5.1. Introduction. 5.2. Common fixed-point theorems. 5.3. Coupled coincidence point theorems. 5.4. References. 6. Introduction to fixed figure problems in fuzzy metric spaces. 6.1. Introduction. 6.2. The Fixed-Circle Problem on Fuzzy Metric Spaces. 6.3. The Fixed-Cassini Curve Problem on Fuzzy Metric Spaces. 6.4. Fixed Point Sets of Quasi-nonexpansive maps. 6.5. References. 7. Applications of fuzzy metrics and fixed-point theorems. 7.1. Introduction. 7.2. Image filtering using fuzzy metrics. 7.3. Applications to fuzzy fixed-point theorems. 7.4. References.

### Biography

Dhananjay Gopal has a doctorate in Mathematics from Guru Ghasidas University, Bilaspur, India, and is currently an Associate Professor of Mathematics at Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur (C.G.) India. He also serves as visiting Professor, at the Department of Mathematics, University of Jaen, Spain. He was an Assistant Professor of Applied Mathematics at S.V. National Institute of Technology, Surat, Gujarat from 2009 to 2020. His research interests include Nonlinear Analysis and Fuzzy Metric Fixed Point Theory.

He is the author and co-author of more than 110 papers in journals, proceedings, and 3 books in the field of metric spaces and fixed-point theory. He is an editorial board member of more than 3 international journals and a regular reviewer of more than 50 journals published by Springer, Elsevier, Taylor & Francis, Wiley, IOS Press, World Scientific, American Mathematical Society, and De Gruyter. He was the guest editor of the special issue " Fixed point theory in abstract metric spaces with generalized contractive conditions; new methods, algorithms, and Applications", in the Journal of Mathematics and the Special Issue on“Nonlinear operator theory and its Applications” in the Journal of function spaces.

Dr. Gopal has active research collaborations with KMUTT, Bangkok, Thammasat University Bangkok, and Jaen University Spain, and in his research pursuits, he has visited South Africa, Thailand, Japan, and Iran.

Juan Martinez Moreno is a Full Professor at the Department of Mathematics, University of Jaen, Spain. His research focuses on topology, fuzzy mathematics, fixed point theory, and their applications. Dr. Juan's work has been published in several journals in the areas of general and applied mathematics and computer science. He also serves as an editor and referee for several mathematics journals.