Existence Of Solutions For Set-Valued Generalized Strong Vector Equilibrium Problems

This paper, we study the set-valued generalized strong vector equilibrium problems, in a real locally convex Huasdorff topological vector space. We introduce the definitions of lower semi cone-continuous and cone-quasi-convex in set-valued mappings. Using these two concepts and Kakutani-Fan-Glicksberg fixed point theorem, we get an existence theorem of solution for set-valued generalized strong vector equilibrium problems. When ternary set-valued mappings degenerate into single-valued mappings, the existence theorem that we get is an improvement of the main result of Fu J.Y [Generalized Vector Quasi-equilibrium Problems, Mathematical Methods of Operations Research, (2000), 52:57-64].