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

  • Authors:

  • Xian-Jun Long;Nan-Jing Huang

  • Affiliations:

  • College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, People's Republic of China 400067;Department of Mathematics, Sichuan University, Chengdu, People's Republic of China 610064

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2009

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Abstract

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.