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自反Banach空间中Ky Fan点的存在性 被引量：4

The Existence of Ky Fan'S Points Over Reflexive Banach Spaces
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摘要 本文对自反Banach空间证明了—个Ky Fan点的存在性定理,作为它的应用,对非合作博弈的Nash平衡点及变分不等式的解给出了几个存在性定理. In this paper, an existence theorem of Ky Fan＇s points is obtained for reflexive Banach spaces. As it＇s applications,some existence theorems for Nash Equilibrium points of noncooperative games and solutions of variartional inequalities are given.
作者 俞建
机构地区 贵州大学数学系
出处 《应用数学学报》 CSCD 北大核心 2008年第1期126-131,共6页 Acta Mathematicae Applicatae Sinica
基金 国家自然科学基金(10561003)资助项目
关键词 自反BANACH空间 KY Fan点 存在性 NASH平衡点 变分不等式 reflexive Banach spaces Ky Fan＇s points existence Nash equilibrium point variartional inequality
分类号 O177.91 [理学—基础数学] O151.21 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Tan K K, Yu J, Yuan X Z. The Stability of Ky Fan's Points. Proc. Amer. Math. Soc., 1995, 123: 1511-1519
  • 2Fan K. A Minimax Inequality and Applications. In: Shisha O (Ed.), Inequality Ⅲ. New York: Academic Press, 1972, 103-113
  • 3Aubin J P, Frankowska H. Set-valued Analysis. Boston: Birkhauser, 1990
  • 4Yu J, Xiang S W. On Essential Components of the Set of Nash Equilibrium Points. Nonlinear Analysis TMA, 1999, 38:259-264
  • 5Kohlberg E, Mertens J F. On the Strategic Stability of Equilibria. Econometrica, 1986, 54:1003-1037
  • 6William R J. Sufficient Conditions for Nash Equilibria in N-Person Games over Relfexive Banach Spaces. J. Opt. Theory Appl., 1980, 30:383-394
  • 7Yu J. On Nash Equilibria in N-Person Games over Relfexive Banach Spaces. J. Opt. Theory Appl., 1992, 73:211-214
  • 8Han J, Huang Z H, Fang S C. Solvability of Variational Inequality Problems. J. Opt. Theory Appl., 2004, 122:501-520
  • 9Han J, Xiu N H, Qi H D. Theory and Algorithm of Nonlinear Complementarity Problems. Shanghai: Shanghai Scientific and Technical Publishers, 1985
  • 10Cea J. Optimisation: Theorie et Algorithmes. Paris: Dunod, 1971

同被引文献82

  • 1俞建.对策论中的本质平衡[J].应用数学学报,1993,16(2):153-157. 被引量：21
  • 2William R J.Sufficient Conditions for Nash Equilibria in N-Person Games over Relfexive Banach Spaces[J].J.Opt.Theory Appl.,1980,30:383-394.
  • 3Yu J.On Nash Equilibria in N-Person Games over Relfexive Banach Spaces[J].J.Opt.Theory Appl.,1992,73:211-214.
  • 4S Y Wang.An existence theorem of a Pareto equilibrium[J].Appl Math Lett,1991,4(3):61-63.
  • 5J Yu,X Z Yuan.The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods[J].Computer.Math.Applic,1998,35(9):19-24.
  • 6H Yang,J Yu.On essential components of the set of weakly Pareto-Nash equilibrium points[J].Applied Math.Letters,2002,15:553-560.
  • 7D.T.Luc.Theory of Vector Optimization[M].Berlin:Springer-Verlag,1989.
  • 8Aliprantis C D and Border K C.Infinite Dimensional Analysis[M].Berlin,Heidelberg:Springer-Verlag,1999.
  • 9Tan K K, Yu J, Yuan X Z. The Stability of Ky Fan's Points. Proc. Amer. Math. Soc., 1995, 123: 1511-1519.
  • 10Fan Ky. A Minmax Inequality and Its Applications. In: Inequalities III, edited by O. Shisha. New York: Academic Press, 1972.

引证文献4

二级引证文献12

应用数学学报
2008年 第1期

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