ON SET-VALUED MIXED VECTOR VARIATIONAL-LIKE INEQUALITIES IN BANACH SPACES

Abstract

In this paper we introduce the concept of generalized $\eta$-pseudomonotone mappings and generalized version of vector mixed variational-like inequalities in Banach spaces. Utilizing Ky Fan's Lemma and Nadler's Lemma, we derive the solvability for this class of vector mixed variational-like inequalities involving generalized $\eta$-pseudomonotone mappings. The results presented in this work are extensions and improvements of some earlier and recent results in the literature.