Gap functions and existence of solutions to generalized vector variational inequalities Original Research Article

In this paper, the gap function for a new class of generalized vector variational inequalities with point-to-set mappings (for short, GVVI) is introduced and the necessary and sufficient conditions for the GVVI are established. In order to derive the existence of solutions for the GVVI, we also introduce the concept of ηη-hh-C(x)C(x)-pseudomonotonicity. By considering the existence of solutions for vector variational inequalities (for short, VVI) with a single-valued function and a continuous selection theorem, we obtain the existence theorem for the GVVI under the assumption of ηη-hh-C(x)C(x)-pseudomonotonicity. The results presented in this paper extend and unify corresponding results of other authors.