# WEAKLY RELAXED $\alpha$-SEMI-PSEUDOMONOTONE SET- VALUED VARIATIONAL-LIKE INEQUALITIES

• Published : 2004.08.01

#### Abstract

In this paper, we introduce weakly relaxed $\alpha$-pseudomonotonicity and weakly relaxed $\alpha$-semi-pseudomonotonicity of set-valued maps. Using the KKM technique, we obtain existence of solutions to the variational-like inequalities with weakly relaxed $\alpha$-pseudomor.otone set-valued maps in reflexive Banach spaces. We also present the solvability of the variational-like inequalities with weakly relaxed $\alpha$-semi-pseudomonotone set-valued maps in arbitrary Banach spaces using Kakutani-Fan-Glicksberg fixed point theorem.