Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (4): 1006-1017.

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Generic Stability of the Solution Set for Symmetric Vector Quasi-equilibrium Problems under the Condition of Cone-convexity

 CHEN Jian-Chen, GONG Xun-Hua   

  1. Department of Mathematics, Nanchang University, Nanchang 330031
  • Received:2007-11-28 Revised:2009-04-15 Online:2010-07-25 Published:2010-07-25
  • Supported by:

    国家自然科学基金(10561007)和江西省自然科学基金(2008GZS0072)资助

Abstract:

In topological vector spaces, a new existence result on the weakly Pareto solutions for vector quasi-equilibrium problem is obtained by the Ky Fan's section theorem. As an application, a new existence theorem of the weakly Pareto solutions for symmetric vector quasi-equilibrium problem is obtained under the condition that its payoff functions are cone-convex. The theorem, under weaker conditions, solves the second problem proposed by Fu in [1], whether there is a weakly Pareto solution for symmetric vector quasi-equilibrium problem when its payoff functions are cone-convex. At last the authors discuss the generic stability of the solution set for symmetric vector quasi-equilibrium problem under the condition of cone-convexity in normed linear spaces.

Key words: Symmetric vector quasi-equilibrium problem, Cone-convex mapping, Generic stability

CLC Number: 

  • 58E35
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