New generalised mixed vector variational-like inequalities with semi-\(\eta\)-pseudomonotonicity (Q2204629)

Summary: In this paper, we introduce the concept of semi-\(\eta\)-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 \textit{S. Plubtieng} and \textit{T. Thammathiwat} [J. Optim. Theory Appl. 162, No. 2, 589--604 (2014; Zbl 1317.47059)]. Few examples are given to justify our new findings.