New generalised mixed vector variational-like inequalities with semi-η-pseudomonotonicity

Abstract

In this paper, we introduce the concept of semi-η-pseudomonotonicity for vector set-valued mappings. Using this concept, and utilising KKM technique and Nadler's Lemma, we establish some existence results for the new generalised mixed vector variational-like inequality problem in reflexive Banach spaces. Our results are the extension and improvement of some of the results given by Plubtieng and Thammathiwat (2014). Few examples are given to justify our new findings.