Fixed Point Results in W-Distance Spaces
Fixed Point Results in W-Distance Spaces is a self-contained and comprehensive reference for advanced fixed-point theory and can serve as a useful guide for related research. The book can be used as a teaching resource for advanced courses on fixed-point theory, which is a modern and important field in mathematics. It would be especially valuable for graduate and postgraduate courses and seminars.
- Written in a concise and fluent style, covers a broad range of topics and includes related topics from research.
- Suitable for researchers and postgraduates.
- Contains brand new results not published elsewhere.
1. Introduction. 1.1. Metric Spaces. 1.2. Banach Contraction Principle. 1.3. Kannan Contraction. 1.4. Ćirićs Quasi-Contraction. 2. Some Basic Properties of W-Distances. 2.1. Definition and Examples. 2.2. Basic Properties of W-Distances. 2.3. More Results on W-Distances. 3. Fixed Point Results in the Framework of W-Distances. 3.1. Basic Fixed Point Results. 3.2. Banach Contraction Principle. 3.3 Rakotch’s Theorem. 3.4 Meir and Keeler’s Theorem. 3.5. Kannan Mappings. 3.6. Ćirićs Quasi-Contraction. 3.7. Fisher Quasi-Contraction. 4. Some Common Fixed Point Results using W-Distances. 4.1. Some Results of Ume and Kim. 4.2. Das and Naik Contraction. 4.3. Common Coupled Fixed Point Results. 4.4. Some of Mohanta’s Results. 4.5. Second Fisher theorem. 5. Best Proximity Points and Various (φ, ψ, p)-Contractive Mappings. 5.1 Best Proximity Points Involving Simulation Functions. 5.2. Best Proximity Points with R-Functions. 5.3. (φ, ψ, p)-Contractive Mappings. 5.4. (φ, ψ, p)-Weakly Contractive Mappings. 5.5. Generalized Weak Contraction Mappings. 5.6. W− ϕ-Kannan Contractions. 6. Miscellaneous Complements. 6.1. Multivalued Mappings. 6.2. Ćirićs Type Contractions at a Point. 6.3. Extension of a Result by Ri. 6.4. Weaker Meir-Keeler Function. 6.5. Contractive Mappings of Integral Type. 6.6 Ekeland’s Variational Principle. 6.7 Some Generalizations and Comments. Bibliography. Index.