Overview
Explores topological fixed point theory for categories of single and multivalued maps
Written for graduate students as well as theoretical and applied
mathematicians interested in fixed point theory, integral equations, ordinary and partial differential equations, and game theory
Develops a method to indicate how to use approximate fixed point theorems to prove the existence of approximate Nash equilibria for non-cooperative games
Includes supplementary material: sn.pub/extras
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The authors continue to present some fixed point theorems in a nonempty closed convex of any Banach algebras or Banach algebras satisfying a sequential condition (P) for the sum and the product of nonlinear weakly sequentially continuous operators, and illustrate the theory by considering functional integral and partial differential equations. The existence of fixed points, nonlinear Leray–Schauder alternatives for different classes of nonlinear (ws)-compact operators (weakly condensing, 1-set weakly contractive, strictly quasi-bounded) defined on an unbounded closed convex subset of a Banach space are also discussed. The authors also examine the existence of nonlinear eigenvalues and eigenvectors, as well as the surjectivity of quasibounded operators. Finally, some approximate fixed point theorems for multivalued mappings defined on Banach spaces. Weak and strong topologies play a role here and both bounded and unbounded regions are considered. The authors explicate a method developed to indicate how to use approximate fixed point theorems to prove the existence of approximate Nash equilibria for non-cooperative games.
Fixed point theory is a powerful and fruitful tool in modern mathematics and may be considered as a core subject in nonlinear analysis. In the last 50 years, fixed point theory has been a flourishing area of research. As such, the monograph begins with an overview of these developments before gravitating towards topics selected to reflect the particular interests of the authors.
Reviews
“This monograph, written by experts in the field and reflecting their particular interests, deals with some developments of fixed point theory for several classes of singlevalued and multivalued maps. … Both graduate students and mathematicians working in fixed point theory, integral equations, ordinary and partial differential equations, game theory, and other related areas will find this book useful and highly instructive.” (Paola Rubbioni, zbMATH 1357.47001, 2017)
“The book, including original contributions of the authors, is addressed to researchers interested in applications of fixed point results (in functional analytic context) to integral equations, ordinary and partial differential equations, game theory, etc. The detailed exposition of the subject and the prerequisites make it appropriate for graduate courses in linear and in nonlinear functional analysis.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (3), 2016)
Authors and Affiliations
About the authors
Afif Ben Amar is Professor in the Department of Mathematics, Faculty of Sciences, at the University Sfax, Tunisia. His research interests include operator theory, partial differential equations, integral equations, and applications of mathematics to the natural sciences. His work has been featured in the Arabian Journal of Mathematics, Afrika Mathematika, and Acta Applicandae Mathematicae.
Bibliographic Information
Book Title: Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications
Authors: Afif Ben Amar, Donal O'Regan
DOI: https://doi.org/10.1007/978-3-319-31948-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-31947-6Published: 13 May 2016
Softcover ISBN: 978-3-319-81162-8Published: 27 May 2018
eBook ISBN: 978-3-319-31948-3Published: 04 May 2016
Edition Number: 1
Number of Pages: X, 194