Open AccessLevitin-Polyak well-posedness of completely generalized mixed variational inequalities in reflexive banach spaces
Author(s) -
Lu-Chuan Ceng,
ChingFeng Wen
Publication year - 2017
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.48.2017.2271
Subject(s) - mathematics , banach space , reflexivity , inequality , variational inequality , space (punctuation) , pure mathematics , mathematical analysis , computer science , social science , sociology , operating system
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 well-posedness 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.