Fixed Point Theory in Ordered Sets and Applications
From Differential and Integral Equations to Game Theory
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Beschreibung
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. It begins with a discussion of some simple examples of the order-theoretic fixed point results along with simple applications from each of the diverse fields. The fixed point theory is then developed and preliminary results on multi-valued variational inequalities regarding the topological and order-theoretical structure of solution sets are covered. This is followed by more advanced material which demonstrates the power of the developed fixed point theory. 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 in 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.
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.
Presents a comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets along with its various interactions with topological structures Considers a wide range of mathematical theories and methods when dealing with applications With numerous illustrations Includes supplementary material: sn.pub/extras
Autor*in
Siegfried Carl
Themen in »Fixed Point Theory in Ordered Sets and Applications«
Inequalities Integration theory Nonlinear analysis Order-theoretic
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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)()