Lower semicontinuity of the solution map to a parametric generalized variational inequality in reflexive banach spaces

Abstract

This paper is concerned with the study of solution stability of a parametric generalized variational inequality in reflexive Banach spaces. Under the requirements that the operator of a unperturbed problem is of class (S) ∈+∈ and operators under consideration are pseudo-monotone and demicontinuous, we show that the solution map of a parametric generalized variational inequality is lower semicontinuous. The obtained results are proved without conditions related to the degree theory and the metric projection. © 2008 Springer Science+Business Media B.V.