The generalized game and the system of generalized vector quasi-equilibrium problems in locally FC-uniform spaces

In this paper, by using a KKM type theorem in FC-space, a new Himmelberg type fixed point theorem for compact and closed set-valued mappings and an existence theorem for equilibrium points for a generalized game in locally FC-uniform spaces without any convexity structure are proved for the first time. By applying the equilibrium existence theorem, some new existence results for solutions for several classes of systems of generalized vector quasi-equilibrium problems are obtained in locally FC-uniform spaces. These results generalize some known results from the literature.