留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

局部G-凸空间内的广义矢量拟平衡问题

丁协平

丁协平. 局部G-凸空间内的广义矢量拟平衡问题[J]. 应用数学和力学, 2005, 26(5): 519-526.
引用本文: 丁协平. 局部G-凸空间内的广义矢量拟平衡问题[J]. 应用数学和力学, 2005, 26(5): 519-526.
DING Xie-ping. Generalized Vector Quasi-Equilibrium Problems in Locally G-Convex Spaces[J]. Applied Mathematics and Mechanics, 2005, 26(5): 519-526.
Citation: DING Xie-ping. Generalized Vector Quasi-Equilibrium Problems in Locally G-Convex Spaces[J]. Applied Mathematics and Mechanics, 2005, 26(5): 519-526.

局部G-凸空间内的广义矢量拟平衡问题

基金项目: 四川省教育厅重点科研基金资助项目(2003A081;SZD0406)
详细信息
    作者简介:

    丁协平(1938- ),男,四川自贡人,教授(E-mail:dingxip@sicnu.edu.cn).

  • 中图分类号: O255;O177.92

Generalized Vector Quasi-Equilibrium Problems in Locally G-Convex Spaces

  • 摘要: 在局部G-凸空间内引入和研究了几类广义矢量拟平衡问题(GVQEP).包含了大多数广义矢量平衡问题,广义矢量变分不等式问题,拟平衡问题和拟变分不等式问题作为特殊情形.首先在局部G-凸空间内对一人对策证明了一个平衡存在性定理.作为应用,在非紧局部G-凸空间内对GVQEP的解建立了某些新的存在定理.这些结果和论证方法与最近文献中的结果和论证方法相比较是新的和完全不同的.
  • [1] LIN Lai-jiu,YU Zenn-tseun.On some equilibrium problems for Multimaps[J].J Comput Appl Math, 2001,129(1/2):171—183. doi: 10.1016/S0377-0427(00)00548-3
    [2] DING Xie-ping.Quasi-variational inequalities and social equilibrium[J].Appl Math Mech,1991,12(7):639—646. doi: 10.1007/BF02018945
    [3] DING Xie-ping.Existence of solutions for quasi-equilibrium problems[J].J Sichuan Normal Univ,1998,21(6):603—608.
    [4] DING Xie-ping.Existence of solutions for quasi-equilibrium problems in noncompact topological spaces[J].Computers Math Appl,2000,39(3/4):13—21.
    [5] DING Xie-ping. Quasi-equilibrium problems with applications to infinite optimization and constrained games in noncompact topological spaces[J].Appl Math Lett,2000,13(3):21—26.
    [6] DING Xie-ping. Quasi-equilibrium problems and constrained multiobjective games in generalized convex spaces[J]. Appl Math Mech,2001,22(2):160—172.
    [7] DING Xie-ping. Maximal element principles on generalized convex spaces and their applications[A].In:Argawal R P Ed.Mathematical Analysis and Applications (4)[C]. London: Taylor & Francis, 2002,149—174.
    [8] LIN Lai-jiu, Park S. On some generalized quasi-equilibrium problems[J].J Math Anal Appl, 1998,224(2): 167—181. doi: 10.1006/jmaa.1998.5964
    [9] CHEN Ming-po, LIN Lai-jiu, Park S. Remarks on generalized quasi-equilibrium problems[J].Nonlinear Anal, 2003,52(2):433—444. doi: 10.1016/S0362-546X(02)00106-2
    [10] Park S. Fixed points and quasi-equilibrium problems[J].Math Computer Modelling,2000,32(11/13):1297—1304. doi: 10.1016/S0895-7177(00)00204-1
    [11] Ansari Q H, Yao J C. An existence result for the generalized vector equilibrium problem[J]. Appl Math Lett, 1999,12(8):53—56.
    [12] Oettli W, Schlager D. Existence of equilibria for g-monotone mappings[A].In:Takahashi W,Tanaka T Eds.Nonlinear Analysis and Convex Analysis[C].Singapore:World Scientific Pub, 1999,26—33.
    [13] DING Xie-ping,Park J Y. Fixed points and generalized vector equilibria in G-convex spaces[J]. Indian J Pure Appl Math,2003,34(6):973—990.
    [14] DING Xie-ping, Park J Y. Generalized vector equilibrium problems in generalized convex spaces[J]. J Optim Theory Appl,2004,120(2):225—235.
    [15] LIN Lai-jiu, YU Zenn-tsuen, Kassay G. Existence of equilibria for multivalued mappings and its application to vectorial equilibria[J].J Optim Theory Appl, 2002,114(1):189—208. doi: 10.1023/A:1015420322818
    [16] Giannessi F.Vector Variational Inequalities and Vector Equilibria[M].London: Kluwer Academic Publishers, 2000,403—422.
    [17] Park S. Fixed points of better admissible maps on generalized convex spaces[J].J Korean Math Soc, 2000,37(6):885—899.
    [18] Park S. Fixed point theorems in locally G-convex spaces[J].Nonlinear Anal, 2002,48(6): 869—875. doi: 10.1016/S0362-546X(00)00220-0
    [19] Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(2): 551—571. doi: 10.1006/jmaa.1997.5388
    [20] Tarafdar E. Fixed point theorems in locally H-convex uniform spaces[J]. Nonlinear Anal,1997,29(9):971—978. doi: 10.1016/S0362-546X(96)00174-5
    [21] Horvath C D. Contractibility and generalized convexity[J].J Math Anal Appl, 1991,156(2):341—357. doi: 10.1016/0022-247X(91)90402-L
    [22] Aliprantis C D, Border K C.Infinite Dimensional Analysis[M].New York: Springer-Verlag, 1994,456—520.
    [23] YUAN Xian-zhi.KKM Theory and Applications in Nonlinear Analysis[M].New York: Marcel Dekker, Inc,1999,229—321.
    [24] Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley & Sons, 1984.
  • 加载中
计量
  • 文章访问数:  2404
  • HTML全文浏览量:  135
  • PDF下载量:  752
  • 被引次数: 0
出版历程
  • 收稿日期:  2003-06-30
  • 修回日期:  2005-01-18
  • 刊出日期:  2005-05-15

目录

    /

    返回文章
    返回