Existence of solutions of generalized vector variational-type inequalities with set-valued mappings

In this paper, we introduce a new class of generalized vector variational-type inequalities with set-valued mappings (GVVTI). First, the solvability of generalized vector variational-type inequalities without monotone assumption is considered in Banach spaces by using Brouwer’s fixed point theorem. Second, by the introduction of the concepts of pseudomonotone, vv-coercive and ηη-hemicontinuous, the solvability of (GVVTI) is obtained with the assumption of ηη-hemicontinuous and pseudomonotone.