Fixed Point Theory in Ordered Sets and Applications From Differential and Integral Equations to Game Theory / [electronic resource] :
by Siegfried Carl, Seppo Heikkilä.
- 1st ed. 2011.
- XIII, 477 p. online resource.
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.
9781441975850
10.1007/978-1-4419-7585-0 doi
Mathematical analysis. Analysis (Mathematics). Game theory. Economic theory. Analysis. Game Theory, Economics, Social and Behav. Sciences. Economic Theory/Quantitative Economics/Mathematical Methods.