This book 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.
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.
Features
- 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. iris 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 Rakotchs Theorem. 3.4 Meir and Keelers
Theorem. 3.5. Kannan Mappings. 3.6. iris 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 Mohantas Results. 4.5. Second
Fisher theorem.
5. Best Proximity Points and Various (, , p)-Contractive
Mappings. 5.1 Best Proximity Points Involving Simulation Functions. 5.2. Best
Proximity Points with R-Functions. 5.3. (, , p)-Contractive Mappings. 5.4.
(, , p)-Weakly Contractive Mappings. 5.5. Generalized Weak Contraction
Mappings. 5.6. W -Kannan Contractions.
6. Miscellaneous Complements. 6.1.
Multivalued Mappings. 6.2. iris 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 Ekelands Variational Principle.
6.7 Some Generalizations and Comments. Bibliography. Index.
Vladimir Rakoevi is a Full Professor at the Department of Mathematics of the Faculty of Sciences and Mathematics at the University of Ni 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.
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