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

Panatda Boonman, Rabian Wangkeeree, Lam Quoc Anh

Abstract

In this paper, we first introduce the concepts of Levitin-Polyak well- posedness and Levitin-Polyak well-posedness in the generalized sense for strong vector mixed quasivariational inequality problems of the Minty type and the Stam- pacchia 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.