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The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems

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Abstract

In this paper, the notion of the generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems are investigated. By using the gap functions of the system of vector quasi-equilibrium problems, we establish the equivalent relationship between the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium problems and that of the minimization problems. We also present some metric characterizations for the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium problems. The results in this paper are new and extend some known results in the literature.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, People’s Republic of China

    Jian-Wen Peng

  2. Department of Mathematics, National Cheng Kung University, Tainan, 701, Taiwan, ROC

    Soon-Yi Wu

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  1. Jian-Wen Peng
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  2. Soon-Yi Wu
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Correspondence to Jian-Wen Peng.

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Peng, JW., Wu, SY. The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems. Optim Lett 4, 501–512 (2010). https://doi.org/10.1007/s11590-010-0179-9

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