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Metric characterizations of α-well-posedness for symmetric quasi-equilibrium problems

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The purpose of this paper is to generalize the concept of α-well-posedness to the symmetric quasi-equilibrium problem. We establish some metric characterizations of α-well-posedness for the symmetric quasi-equilibrium problem. Under some suitable conditions, we prove that the α-well-posedness is equivalent to the existence and uniqueness of solution for the symmetric quasi-equilibrium problems. The corresponding concept of α-well-posedness in the generalized sense is also investigated for the symmetric quasi-equilibrium problem having more than one solution. The results presented in this paper generalize and improve some known results in the literature.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Xian-jun Long

  2. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China

    Nan-jing Huang

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  1. Xian-jun Long
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  2. Nan-jing Huang
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Correspondence to Nan-jing Huang.

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Long, Xj., Huang, Nj. Metric characterizations of α-well-posedness for symmetric quasi-equilibrium problems. J Glob Optim 45, 459–471 (2009). https://doi.org/10.1007/s10898-008-9385-8

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