A generalized mixed vector variational-like inequality problem

In this paper, we introduce relaxed ηη-αα-PP-monotone mapping, and by utilizing KKM technique and Nadler’s Lemma we establish some existence results for the generalized mixed vector variational-like inequality problem. Further, we give the concepts of ηη-complete semicontinuity and ηη-strong semicontinuity and prove the solvability for generalized mixed vector variational-like inequality problem without monotonicity assumption by applying the Brouwer’s fixed point theorem. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature.