Existences of solution for the implicit multi-valued vector equilibrium problem

Abstract

In this paper, we consider a class of implicit multi-valued vector equilibrium problems, which includes a number of equilibrium problems, such as implicit vector equilibrium, multi-valued variational inequalities, vector variational inequalities and vector complementarity problems and so on. By using the Fan fixed point theorem, the existence of their solution in the setting of topological vector spaces will be established and proved. These results extend and unify some known results obtained in implicit vector equilibrium problems, multi-valued vector variational inequality problems and vector variational inequality problems.