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

Abstract

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 a generalized Himmelberg type fixed point theorem for a set–valued mapping with KKM–property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC–spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi–equilibrium problems are proved in locally FC–spaces. These theorems improve, unify and generalize many known results in the literatures.