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.
- 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.