Uniqueness and stability of the solution for strongly pseudomonotone variational inequalities in Banach spaces

Abstract

In this paper, we prove an existence and uniqueness theorem of the solution for strongly pseudomonotone variational inequalities in reflexive Banach spaces. Based on this result, and investigate the stability behavior of the perturbed variational inequalities. Moreover, we obtain an existence theorem of solutions for strongly quasimonotone variational inequalities in finite dimensional spaces.

Keywords

Variational inequality / strong pseudomonotonicity / strong quasimonotonicity / existence and uniqueness / stability

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