W-G-F-KKM mapping, intersection theorems and minimax inequalities in FC-space

Abstract

By using basic KKM theorem, a new matching theorem and some minimax inequalities for set-valued mappings defined on the FC-spaces are proved under very weak assumptions. These results generalized many known results from the recent literature.

A Matching Theorem in FC-Spaces with the Application to Coincidence Questions

“…Following Ding et al [1][2][3][4][5][6][7][8], (X, N ϕ ) is said to be an FC-space if X is a topological space such that for each…”

“…In 2007, Zhang et al [2] established an existence theorem of maximal elements, some new collectively fixed-point theorems and some new theorems about minimax inequalities in FC-spaces. Tang et al [3] introduced W-G-F-KKM mappings, and proved a new matching theorem and some minimax inequalities. In 2008, Ding [4] proved a new Himmelberg type fixed point theorem and an existence theorem for equilibrium points for a generalized game in locally FC-uniform spaces, and obtained some new existence results for solutions for several classes of systems of generalized vector quasi-equilibrium problems in locally FC-uniform spaces.…”

Some New Coincidence Theorems in Product GFC-Spaces with Applications

“…Recently, Ding [1,2], X. P. Ding and T. M. Ding [3], Tang et al [4], Fang and Huang [5] established some collective fixed point theorems, coincidence theorems, and KKM-type theorems for the families of set-valued mappings, which are defined on FC-spaces or product FC-spaces without any convexity structure.…”