Well-posedness of generalized vector variational inequality problem via topological approach

In this paper, we discuss well-posedness for a generalized vector variational inequality problem (GVVIP, in short) in the framework of topological vector spaces. Unlike in the available literature, we have adopted a topological approach using admissibility and convergence of nets, instead of monotonicity and convexity etc of the function involved. We provide necessary and sufficient conditions for a GVVIP to be well-posed in generalized sense. We give a characterization for GVVIP to be well-posed in generalized sense in terms of the upper semi-continuity of the approximate solution set map. Also, we provide some necessary conditions for a GVVIP to be well-posed in generalized sense in terms of Painleve-Kuratowski convergence.