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.
Table of Contents
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.
Vladimir Rakočević is a Full Professor at the Department of Mathematics of the Faculty of Sciences and Mathematics at the University of Niš in Serbia, and a Corresponding Member of the Serbian Academy of Sciences and Arts (SANU) in Belgrade, Serbia. He earned his Ph.D. in mathematics at the Faculty of Sciences of Belgrade University, Serbia, in 1984; the title of his thesis was Essential Spectra and Banach Algebras. He was a visiting professor at several universities and scientific institutions in various countries. Furthermore, he participated as an invited or keynote speaker in numerous international scientific conferences and congresses. He is a member of the editorial boards of many journals of international repute. His list of publications contains more than 190 research papers in international journals, and he was included in Thomson Reuters’ list of Highly Cited Authors in 2014. He is the (co-)author of eight books. He supervised 8 Ph.D., and more than 50 B.Sc. and M.Sc. theses in mathematics. His research interests include functional analysis, fixed point theory, operator theory, linear algebra and summability.