Maximal elements of GKKM-majorized mappings in product FC-spaces and applications (II)

This paper is a continuation of the preceding paper of the author. Four classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces. The notions of Ci(x)-FC-quasiconvexity, Ci(x)-quasiconvexity and Ci(x)-quasiconvexity-like for set-valued mappings are introduced in FC-spaces. By applying these notions and the equilibrium existence theorems for generalized games obtained in the author's preceding paper, some new existence theorems of solutions for these systems of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.