Existence of the solution of the stereotype vector variational inequalities in stereotype vector spaces using indicator function

Abstract

In this paper the concept of reflexivity for the contractible topological vector spaces (called stereotype vector spaces) is introduced in the sense of vector stereotype function and then defined various inequality problems depends on the vector evaluation map in the stereotype vector spaces, such as stereotype vector variational inequalities, stereotype dual vector variational inequalities and stereotype vector complementari-ties in ordered topological vector spaces. The existence of the weak* solution of these problems is studied in the presence of stereotype monotonicity and weak* hemiconti-nuity of the vector evaluation map. Using the property of weak* indicator function, the existence of the solution of these problems is established.