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Full Description
This self-contained monograph presents an overview of fuzzy operator theory in mathematical analysis. Concepts, principles, methods, techniques, and applications of fuzzy operator theory are unified in this book to provide an introduction to graduate students and researchers in mathematics, applied sciences, physics, engineering, optimization, and operations research. New approaches to fuzzy operator theory and fixed point theory with applications to fuzzy metric spaces, fuzzy normed spaces, partially ordered fuzzy metric spaces, fuzzy normed algebras, and non-Archimedean fuzzy metric spaces are presented. Surveys are provided on: Basic theory of fuzzy metric and normed spaces and its topology, fuzzy normed and Banach spaces, linear operators, fundamental theorems (open mapping and closed graph), applications of contractions and fixed point theory, approximation theory and best proximity theory, fuzzy metric type space, topology and applications.
Contents
1. Preliminaries.- 2. Fuzzy normed spaces and fuzzy metric spaces.- 3. Further properties of fuzzy Banach spaces.- 4. Fundamental theorems in fuzzy normed spaces.- 5. Fixed point theorems in fuzzy metric spaces.- 6. Generalized distances and fixed point theorems in fuzzy metric spaces.- 7. Fixed point theorems in partially ordered fuzzy metric spaces.- 8. Fixed point theorems in fuzzy normed spaces.- 9. Approximation theory in fuzzy metric spaces.- 10. Topologies and fixed points in fuzzy metric-type spaces.- 11. Operator theory and fixed points in fuzzy normed algebras and applications.- 12. Fixed points in non-Archimedean fuzzy metric spaces.- 13. Coincidence points for set-valued mappings in fuzzy metric spaces.
