Abstract
In this chapter, we discuss several variants of variational inequality problems that exist in the literature. We also discuss solutions to the vector variational inequality problem and generalized vector variational inequality problem in a more general framework, using a topological approach. We consider X and Y as topological vector spaces and provide different sets of conditions for the existence of solutions in the light of upper semi-continuity and lower semi-continuity, respectively. Admissibility of function space topology and convergence of net of sets are used as major tools towards achieving this goal. Topological properties of the solution sets of VVI and GVVI problems are also discussed.
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