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This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained.Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.
List of contents
Preface.- Introduction.- Fundamental Order-Theoretic Principles.- Multi-Valued Variational Inequalities.- Discontinuous Multi-Valued Elliptic Problems.- Discontinutous Multi-Valued Evolutionary Problems.- Banach-Valued Ordinary Differential Equations.- Banach-Valued Integral Equations.- Game Theory.- Appendix.- List of Symbols.- References.- Index.
Summary
This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained.
Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.
Additional text
From the reviews:
“The book provides a self-contained exposition of an order-theoretic fixed point theory in partially ordered sets together with its interactions with topological structures. … The book is well written and provides a very detailed study of theoretic topics along with many illustrative examples and applications of various types covering an immense range of problems. … the book is very well designed for studying nonlinear problems via a fixed point approach. Both graduate students and mathematicians … will find this book attractive, useful and highly instructive.” (Wojciech Kryszewski, Mathematical Reviews, Issue 2012 c)
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From the reviews:
"The book provides a self-contained exposition of an order-theoretic fixed point theory in partially ordered sets together with its interactions with topological structures. ... The book is well written and provides a very detailed study of theoretic topics along with many illustrative examples and applications of various types covering an immense range of problems. ... the book is very well designed for studying nonlinear problems via a fixed point approach. Both graduate students and mathematicians ... will find this book attractive, useful and highly instructive." (Wojciech Kryszewski, Mathematical Reviews, Issue 2012 c)
