LEVITIN-POLYAKWELL-POSEDNESS OF COMPLETELY GENERALIZED MIXED VARIATIONAL INEQUALITIES IN REFLEXIVE BANACH SPACES

10.5556/j.tkjm.48.2017.2271

LU-CHUAN CENG；CHING-FENG WEN

Tamkang Journal of Mathematics

48卷1期（2017 / 03 / 01）

95 - 122

英文

Let X be a real reflexive Banach space. In this paper, we first introduce the concept of Levitin-Polyak well-posedness of a completely generalized mixed variational inequality in X, and establish some characterizations of its Levitin-Polyak well-posedness. Under suitable conditions, we prove that the Levitin-Polyak well-posedness of a completely generalized mixed variational inequality is equivalent both to the Levitin-Polyak well-posedness of a corresponding inclusion problem and to the Levitin-Polyak wellposedness of a corresponding fixed point problem. We also derive some conditions under which a completely generalized mixed variational inequality in X is Levitin-Polyak well-posed. Our results improve, extend and develop the early and recent ones in the literature.