Vector Variational-Like Inequalities with Generalized Semimonotone Mappings

Abstract EN

We introduce the concepts of generalized relaxed monotonicity and generalized relaxed semimonotonicity.

We consider a class of generalized vector variationa-llike inequality problem involving generalized relaxed semimonotone mapping.

By using Kakutani-Fan-Glicksberg’s fixed-point theorem, we prove the solvability for this class of vector variational-like inequality with relaxed monotonicity assumptions.

The results presented in this paper generalize some known results for vector variational inequality in recent years.