Topological Variants of Vector Variational Inequality Problem

Abstract

In this paper, we provide a couple of solutions for the vector variational inequality problem, adopting a topological approach. We consider here a more general framework, where X and Y are topological vector spaces. Topological concepts including continuity, compactness, closedness, and so on are used for obtaining our results. The condition of admissibility of the function space topology is found to play an important role in achieving the results. It is found that the solution sets so obtained are closed as well as compact.