KKM Type Theorems And Generalized Vector Equilibrium Problems In FC-Spaces

This paper mainly further studies several focus problems of nonlinear functional analysis in finitely continuous topological spaces (in short, FC-spaces) without any convexity and linear structure, unites and generalizes some known results in recent literature. At first, we establish some new KKM type theorems involving admissible set-valued mappings and the set-valued mapping with compactly local intersection property in FC-spaces. As applications, some new coincidence theorems and fixed point theorems are proved in FC-spaces. Next, we introduce some new systems of quasi-equilibrium problems in FC-spaces. By applying the fixed point theorem in FC-spaces due to the above, some new existence theorems of systems of quasi-equilibrium problems are obtained. Eventually, we introduce a class of FC-KKM (X, Y) in FC-spaces, and establish some new KKM type theorems and coincidence theorems involving the class of FC-KKM (X, Y) in FC-spaces. By applying these results, we prove some new existence theorems of equilibrium points for abstract generalized vector equilibrium problems.