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

Authors

  • Lu-Chuan Ceng
  • Ching-Feng Wen

DOI:

https://doi.org/10.5556/j.tkjm.48.2017.2271

Keywords:

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

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.

Author Biographies

Lu-Chuan Ceng

Department ofMathematics, Shanghai Normal University, Shanghai 200234, China.

Ching-Feng Wen

Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, KaohsiungMedical University, Kaohsiung 807, Taiwan.

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Published

2017-03-30

How to Cite

Ceng, L.-C., & Wen, C.-F. (2017). Levitin-Polyak well-posedness of completely generalized mixed variational inequalities in reflexive banach spaces. Tamkang Journal of Mathematics, 48(1), 95–121. https://doi.org/10.5556/j.tkjm.48.2017.2271

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Papers