As a generalization of Fan-Glicksberg fixed point theorem,a new existence theorem of fixed point theorem for set-valued mapping is proved.

This paper first study the existence of solutions for generalized mixed vector quasi-equilibrium problems in locally convex Hausdorff topological vector space by using nonlinear scalariztion function and Kakubani-Fan-Glicksberg fixed pointed theorem.

By using this theorem a topological Kakutani-Fan-Glicksberg`s Fixed Point Theorem without linear structure is obtained.

By using Fan-Browder fixed point theorem and FKKM theorem,some existence theorems of them are obtained,which extend and unify corresponding results of Fu-Wan in generalized vector equilibrium problems with set-valued mappings.