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

In this paper, several kinds of generalized vector quasi-equilibrium problems are introduced and studied in abstract convex spaces. Using the properties of Γ-convex and $\mathfrak{KC}$-maps, some sufficient conditions are given to guarantee the existence of solutions in connection with these generalized vector quasi-equilibrium problems. As applications, some existence theorems of solutions for the generalized semi-infinite programs with vector quasi-equilibrium constraints are also given. [ABSTRACT FROM AUTHOR]