On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping

Abstract EN

We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings.

Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established.

Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.