Carl S., Heikkilä S. Fixed Point Theory in Ordered Sets and Applications: From Differential and Integral Equations to Game Theory

Springer, 2011. — 492 p. — ISBN: 978-1-4419-7584-3.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.Fundamental Order-Theoretic Principles
Multi-Valued Variational Inequalities
Discontinuous Multi-Valued Elliptic Problems
Discontinuous Multi-Valued Evolutionary Problems
Banach-Valued Ordinary Differential Equations
Banach-Valued Integral Equations
Game Theory