Some new generalizations of nonempty intersection theorems without convexity assumptions and essential stability of their solution set with applications

摘要

As a generalization of the KKM theorem in (Yang and Pu in J. Optim. Theory Appl. 154:17-29 2012), we propose some new nonempty intersection theorems for an infinite family of set-valued mappings without convexity assumptions, and consider generic stability and essential components of solutions of a nonempty intersection theorem for an infinite family of set-valued mappings without convexity assumptions. This paper is an attempt to establish analogue results for the class of equilibria removing convexity assumptions. As applications, we deduce the corresponding results for Ky Fan’s points, Nash equilibrium and variational relations. MSC:49J53, 49J40.