Fuzzy Operator Theory in Mathematical Analysis

Preface......Page 3
Contents......Page 4
Acronyms......Page 8
1.1 Triangular Norms......Page 9
1.2 Fuzzy Sets......Page 14
1.3 Triangular Norms on Lattices......Page 16
2.1 Fuzzy Normed Spaces......Page 18
2.2 Fuzzy Topological Structures......Page 25
2.3 Non-Archimedean Fuzzy Normed Spaces......Page 40
2.4 Intuitionistic Fuzzy Inner Product Spaces......Page 42
2.4.1 Basic Properties and Results......Page 44
2.4.2 Orthogonality......Page 47
3.1 Finite Dimensional Fuzzy Banach Spaces......Page 51
3.2 Fuzzy Quotient Spaces......Page 54
3.3 Linear Operators......Page 57
3.3.1 Bounded and Continuous Linear Operators......Page 58
3.4.1 Fuzzy Norms of Operators......Page 60
3.4.2 Fuzzy Operator Spaces......Page 64
3.5 Compact Operators......Page 68
4.1 Open Mapping Theorem......Page 69
4.2 Closed Graph Theorem......Page 72
5.1 Fixed Point Theorems for Weak Compatible Mappings......Page 74
5.2 R-Weakly Commuting Mappings in Intuitionistic Fuzzy Metric Spaces......Page 84
5.3 Common Fixed Point Theorems for Six Mappings in Three Fuzzy Metric Spaces......Page 88
5.4 Jungck's Theorem in L-Fuzzy Metric Spaces......Page 99
5.5 Hyper L-Fuzzy Metric Spaces......Page 107
5.5.1 Banach's Fixed Point Theorem in MHL-Fuzzy Metric Spaces......Page 110
5.5.2 Kannan's Fixed Point Theorem in MHL-Fuzzy Metric Spaces......Page 113
5.6 Applications of Fixed Point Theorems in Intuitionistic Fuzzy Quasi-Metric Spaces......Page 117
5.6.2 G-Bicompleteness in Non-Archimedean Intuitionistic Fuzzy Quasi-Metric Spaces......Page 120
5.6.3 Applications to the Domain of Words......Page 121
5.7 Gauge Functions and Fixed Point Theorems......Page 124
5.8 Common Point Theorems in Fuzzy Metric Spaces Using the CLRg-Property......Page 131
5.8.1 Auxiliary Results......Page 135
5.8.2 Common Fixed Point Theorems for the Mappings with the CLRg-Property......Page 139
5.9 Fuzzy ψ-Contractive Sequences and Fixed Point Theorems......Page 146
5.9.1 Fixed Point Theorems for Fuzzy ψ-Contractive Mappings......Page 149
6.1 ρ-Distances in Fuzzy Metric Spaces......Page 159
6.1.1 Fixed Point Theorems by the ρ-Distance-I......Page 162
6.2 ρ-Distances on L-Fuzzy Metric Spaces......Page 165
6.3 Fixed Point Theorems by the ρ-Distance-II......Page 176
7 Fixed Point Theorems in Partially Ordered Fuzzy Metric Spaces......Page 181
7.1 Monotone Generalized Contractions......Page 182
7.1.1 Fixed Points in Partially Ordered Fuzzy Metric Spaces......Page 183
7.1.2 Applications in L-Fuzzy Metric Spaces......Page 190
7.2 M-Fuzzy Monotone Generalized Contractions......Page 197
7.3 Common Fixed Point Theorems for φ-Contractions......Page 208
7.3.1 Some Lemmas......Page 209
7.3.2 Fixed Point Theorems......Page 213
7.4 Set-Valued Mappings......Page 221
7.4.1 Coincidence Point and Fixed Point Theorems......Page 222
7.5 Multi-Valued Contractions......Page 238
7.5.1 Applications to Differential Inclusions......Page 245
7.6 Multidimensional Coincidence Points for Compatible Mappings......Page 248
7.6.1 Partial Orders on Xn......Page 249
7.6.2 Mixed Monotone Mappings and Coincidence Points......Page 250
7.6.3 Coincidence Point Theorems......Page 251
7.6.4 Uniqueness of Φ-Coincidence Points......Page 262
8.1 Tripled Coincidence Point Theorems in L-Fuzzy Normed Spaces......Page 266
8.1.1 Applications on Triple Fixed Points......Page 277
8.2 Fixed Point Theorems in IFIP-Spaces......Page 279
8.2.1 Applications of Fixed Points......Page 284
9.1  Nonlinear Approximation Theory......Page 287
9.2 On Convergence of the Ishikawa Type Iteration......Page 291
9.3 Best Proximity Point in Fuzzy Metric Spaces......Page 295
9.4 Fuzzy Proximal Cyclic Contractions......Page 301
9.4.1 Fuzzy Proximal Contractions......Page 303
10.1 Extensions of Metric Spaces......Page 312
10.2 Topologies of Fuzzy Metric-Type Spaces......Page 316
10.3 Common Fixed Point Theorems in Fuzzy Metric-Type Spaces......Page 332
10.3.1 Applications to Integral Equations......Page 337
11.1 Fuzzy Normed Algebras......Page 339
11.2 Fixed Point Theorems in Banach Fuzzy Normed Spaces......Page 341
12 Fixed Points in Non-Archimedean Fuzzy Metric Spaces......Page 347
12.1 Fixed Points in Weak Non-Archimedean Fuzzy Metric Spaces......Page 348
12.1.1 Topologies Induced by Weak Non-Archimedean Fuzzy Metrics......Page 349
12.1.2 Fixed Point Theorems for ψ-Contractive Mappings......Page 352
12.2.1 Fuzzy Metric-Like Spaces and Non-Archimedean Fuzzy Metric-Like Spaces......Page 359
12.2.2 Fixed Points in Non-Archimedean Fuzzy Metric-Like Spaces......Page 365
12.2.3 Applications......Page 370
12.3.1 Fixed Point Theorems......Page 373
13.1 Some Definitions and Lemmas......Page 382
13.2 Coincidence Points in Fuzzy Metric Spaces......Page 386
13.3 Ekeland's Variational Principle......Page 391
13.4 The Equivalence Relation......Page 393
13.5 Applications to Menger PM-Spaces......Page 394
Refs......Page 399
Index......Page 405