Existence of Solutions for New Systems of Generalized Mixed Vector Variational-like Inequalities in Reflexive Banach Spaces

Somyot Plubtieng, Wanna Sriprad

Abstract

In this paper, we introduce and study a new type of generalized mixed vector variational-like inequalities and a new type of system of generalized mixed vector variational-like inequalities in reflexive Banach spaces. Firstly, we introduce the new concept of pseudo-monotonicity for vector multi-valued mappings, and prove an existence theorem of solution for generalized mixed vector variational-like inequalities by using the Fan-KKM theorem. Secondly, we introduce a new type of system of generalized mixed vector variational-like inequalities and by using the Kakutani-Fan-Glicksberg fixed point theorem, some new existence results of solution for system of generalized mixed vector variational-like inequalities are obtained under some suitable conditions.