System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces

摘要

A new class of locally finite continuous topological spaces(for short, locally FC-spaces)and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying ageneralized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due tothe author, a collectively fixed point and an equilibrium existence theorem of generalized game are firstproved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, somenew existence theorems of equilibrium points for the system of generalized vector quasi-equilibriumproblems are proved in locally FC-spaces. These theorems improve, unify and generalize many knownresults in the literatures.