Levitin–Polyak well-posedness of a generalized mixed variational inequality in Banach spaces

Abstract

In this paper, we first introduce the concept of Levitin–Polyak well-posedness of a generalized mixed variational inequality in Banach spaces and establish some characterizations of its Levitin–Polyak well-posedness. Under suitable conditions, we prove that the Levitin–Polyak well-posedness of a generalized mixed variational inequality is equivalent to the Levitin–Polyak well-posedness of a corresponding inclusion problem and a corresponding fixed point problem. We also derive some conditions under which a generalized mixed variational inequality in Banach spaces is Levitin–Polyak well-posed.