New systems of generalized vector quasi-equilibrium problems in product FC-spaces

The notions of C _i (x)-FC-diagonally quasiconvex, C _i (x)-FC-quasiconvex and C _i (x)-FC-quasiconvex-like for set-valued mappings are introduced in FC-spaces without convexity structure. By applying these notions and a maximal element theorem for a family of set-valued mappings on product FC-space due to author, some new existence theorems of solutions for four new classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. These results improve and generalize some recent known results in literature to noncompact FC-spaces.