Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications

In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. By virtue of the properties of Γ-convex and KC-map, we give some sufficient conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. As application, we show an existence theorem of solutions for the generalized semi-infinite programs with generalized symmetric vector quasi-equilibrium constraints.