Levitin-Polyak well-posedness of completely generalized mixed variational inequalities in reflexive banach spaces

Lu-Chuan Ceng, Ching-Feng Wen

Abstract


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.

Keywords


Completely generalized mixed variational inequality; Inclusion problem; Fixed point problem; Levitin-Polyak well-posedness.

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References


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DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.2271

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