Levitin-Polyak Well-Posedness for Strong Vector Mixed Quasivariational Inequality Problems

Abstract

In this paper, we first introduce the concepts of Levitin-Polyak wellposedness and Levitin-Polyak well-posedness in the generalized sense for strong vector mixed quasivariational inequality problems of the Minty type and the Stampacchia type (for short, (MQVI) and (SQVI), respectively). Sufficient conditions for such problems to be Levitin-Polyak well-posedness are established. We also introduce the gap functions for (MQVI) and (SQVI) and study some properties which are used to study the Levitin-Polyak well-posedness for such problems.