Applications of Generalized Variational and Quasivariational Inequalities with Operator Solutions in a TVS

Abstract

In a recent paper, Domokos and Kolumban introduced variational inequalities with operator solutions to provide a unified approach to several kinds of variational inequalities and vector variational inequalities in Banach spaces. Inspired by their work, in a former paper, we extended the scheme of vector variational inequalities with operator solutions from the single-valued case to the multivalued one and provided some applications to generalized vector variational inequalities and generalized quasivector variational inequalities in normed spaces. As a continuation of the former work, in this paper, we further extend those results to more general and tangible cases in the context of Hausdorff topological vector spaces or locally convex spaces.