Topological Methods For Set-valued Nonlinear AnalysisThis book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems.Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings. |
Contents
| 1 | |
| 9 | |
3 Some Fixed Point Theorems in Partially Ordered Sets | 113 |
4 Topological Fixed Point Theorems | 151 |
5 Variational and Quasivariational Inequalities in Topological Vector Spaces and Generalized Games | 265 |
6 Best Approximation and Fixed Point Theorems for SetValued Mappings in Topological Vector Spaces | 447 |
7 Degree Theories for SetValued Mappings | 463 |
8 Nonexpansive Types of Mappings and Fixed Point Theorems in Locally Convex Topological Vector Spaces | 563 |
| 583 | |
| 605 | |
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Topological Methods for Set-valued Nonlinear Analysis Enayet Ullah Tarafdar,Mohammad Showkat Rahim Chowdhury No preview available - 2008 |
Common terms and phrases
a e X assume assumption Banach space bounded subset Chowdhury closed conver closed subset co(A compact conver subset compact subset compactly open contraction mapping Corollary defined Definition denote Ding eaſists equation equilibrium point existence theorem exists a point finite subset fixed point theorem function h(yo Hausdorff topological vector Hence implies inf Re(w KP(I Lemma Let f line segments linear lower semicontinuous mapping f metric space monotone non-empty closed non-empty compact subset nonempty compact nonempty conver nonempty subset norm open neighborhood open set paracompact Proof prove Re(p Re(u result satisfies sequence set-valued mapping solution Suppose Tarafdar topological space topological vector space uniform space upper semicontinuous valued mapping variational inequalities weak topology weakly compact