Fuzzy operator theory in mathematical analysis / Yeol Je Cho, Themistocles M. Rassias, Reza Saadati.
Cho, Yeol Je, author.; Rassias, Themistocles M., 1951- author.; Saadati, Reza, author.
2018
QA9.64
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Title
Fuzzy operator theory in mathematical analysis / Yeol Je Cho, Themistocles M. Rassias, Reza Saadati.
Author
Cho, Yeol Je, author.
ISBN
9783319935010 (electronic book)
3319935011 (electronic book)
9783319934990
3319934996
Published
Cham : Springer, 2018.
Language
English
Description
1 online resource
Call Number
QA9.64
Dewey Decimal Classification
511.3/223
Summary
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.-- Provided by publisher.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (viewed August 15, 2018)
Added Author
Rassias, Themistocles M., 1951- author.
Saadati, Reza, author.
Available in Other Form
Print version: 9783319934990
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Intro; Preface; Acknowledgments; Contents; Acronyms; 1 Preliminaries; 1.1 Triangular Norms; 1.2 Fuzzy Sets; 1.3 Triangular Norms on Lattices; 2 Fuzzy Normed Spaces and Fuzzy Metric Spaces; 2.1 Fuzzy Normed Spaces; 2.2 Fuzzy Topological Structures; 2.3 Non-Archimedean Fuzzy Normed Spaces; 2.4 Intuitionistic Fuzzy Inner Product Spaces; 2.4.1 Basic Properties and Results; 2.4.2 Orthogonality; 3 Further Properties of Fuzzy Banach Spaces; 3.1 Finite Dimensional Fuzzy Banach Spaces; 3.2 Fuzzy Quotient Spaces; 3.3 Linear Operators; 3.3.1 Bounded and Continuous Linear Operators

3.4 Fuzzy Compact Operators3.4.1 Fuzzy Norms of Operators; 3.4.2 Fuzzy Operator Spaces; 3.5 Compact Operators; 4 Fundamental Theorems in Fuzzy Normed Spaces; 4.1 Open Mapping Theorem; 4.2 Closed Graph Theorem; 5 Fixed Point Theorems in Fuzzy Metric Spaces; 5.1 Fixed Point Theorems for Weak Compatible Mappings; 5.2 R-Weakly Commuting Mappings in Intuitionistic Fuzzy Metric Spaces; 5.3 Common Fixed Point Theorems for Six Mappings in Three Fuzzy Metric Spaces; 5.4 Jungck's Theorem in L-Fuzzy Metric Spaces; 5.5 Hyper L-Fuzzy Metric Spaces

5.5.1 Banach's Fixed Point Theorem in MHL-Fuzzy Metric Spaces5.5.2 Kannan's Fixed Point Theorem in MHL-Fuzzy Metric Spaces; 5.6 Applications of Fixed Point Theorems in Intuitionistic Fuzzy Quasi-Metric Spaces; 5.6.1 Banach's Fixed Point Theorem in Intuitionistic Fuzzy Quasi-Metric Spaces; 5.6.2 G-Bicompleteness in Non-Archimedean Intuitionistic Fuzzy Quasi-Metric Spaces; 5.6.3 Applications to the Domain of Words; 5.7 Gauge Functions and Fixed Point Theorems; 5.8 Common Point Theorems in Fuzzy Metric Spaces Using the CLRg-Property; 5.8.1 Auxiliary Results

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