Fixed Point Theory in Ordered Sets and Applications [electronic resource] : From Differential and Integral Equations to Game Theory /
Carl, Siegfried.author.
Heikkilä, Seppo.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
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.
Mathematical analysis.
Analysis (Mathematics).
Game theory.
Economic theory.
Analysis.
Game Theory, Economics, Social and Behav. Sciences.
Economic Theory/Quantitative Economics/Mathematical Methods.