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FC-一致空间内的广义约束多目标对策

丁协平 黎进三 姚任之

丁协平, 黎进三, 姚任之. 局部FC-一致空间内的广义约束多目标对策[J]. 应用数学和力学, 2008, 29(3): 272-280.
引用本文: 丁协平, 黎进三, 姚任之. 局部FC-一致空间内的广义约束多目标对策[J]. 应用数学和力学, 2008, 29(3): 272-280.
DING Xie-ping, Lee Chin-san, YAO Jen-chih. Generalized Constrained Multiobjective Games in Locally FC-Uniform Spaces[J]. Applied Mathematics and Mechanics, 2008, 29(3): 272-280.
Citation: DING Xie-ping, Lee Chin-san, YAO Jen-chih. Generalized Constrained Multiobjective Games in Locally FC-Uniform Spaces[J]. Applied Mathematics and Mechanics, 2008, 29(3): 272-280.

局部FC-一致空间内的广义约束多目标对策

基金项目: 四川省教育厅重点科研基金资助项目(07ZA092);台湾科学委员会基金项目
详细信息
    作者简介:

    丁协平(1938- ),男,自贡人,教授(联系人.Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com);黎进三(1950- ),男,高雄人,教授;姚任之(1959- ),男,高雄人,教授,博士生导师.

  • 中图分类号: 221.2;O177.92

Generalized Constrained Multiobjective Games in Locally FC-Uniform Spaces

  • 摘要: 在没有任何凸性结构的局部FC-一致空间内引入和研究了一类新的广义约束多目标对策,其中局中人数可以是有限或无限的和所有的支付函数可以取值于无限维空间.利用在局部FC-一致空间内得到的一个Himmelberg型不动点定理,在局部FC-一致空间内对广义约束多目标对策建立了某些弱Pareto平衡存在性定理.这些定理改进,统一和推广了最近文献中相应结果.
  • [1] Szidarovszky F,Gershon M E,Duckstein L.Techniques for Multiobjective Decision Marking in System Management[M].Amsterdam, Holland:Elsevier,1986.
    [2] Zeleny M.Game with multiple payoffs[J].International J Game Theory,1976,4(1):179-191.
    [3] Bergstresser K, Yu P L.Domination structures and multicriteria problem in N-person games[J].Theory and Decision,1977,8(1):5-47. doi: 10.1007/BF00133085
    [4] Borm P E M, Tijs S H, Van Den Aarssen J C M. Pareto equilibrium in multiobjective games[J].Methods of Operations Research,1990,60(1):303-312.
    [5] Yu P L.Second-order game problems: Decision dynamics in gaming phenomena[J].J Optim Theory Appl,1979,27(1):147-166. doi: 10.1007/BF00933332
    [6] Chose D, Prasad U R. Solution concepts in two-person multicriteria games[J].J Optim Theory Appl,1989,63(1):167-189. doi: 10.1007/BF00939572
    [7] Wang S Y. An existence theorem of a Parteo equilibrium[J].Appl Math Lett,1991,4(1):61-63.
    [8] Wang S Y.Existence of a Parteo equilibrium[J].J Optim Theory Appl,1993,79(2):373-384. doi: 10.1007/BF00940586
    [9] Wang S Y, Li Z. Pareto equilibria in multicriteria metagames[J].Top,1995,3(2):247-263. doi: 10.1007/BF02568588
    [10] DING Xie-ping.Parteo equilibria of multicriteria games without compactness, continuity and concavity[J].Appl Math Mech,1996,17(9):847-854. doi: 10.1007/BF00127184
    [11] Yuan X Z, Tarafdar E.Non-compact Pareto equilibria for multiobjective games[J].J Math Anal Appl,1996,204(1):156-163. doi: 10.1006/jmaa.1996.0429
    [12] Yu J, Yuan X Z.The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods[J].Comput Math Appl,1998,35(9):17-24.
    [13] DING Xie-ping. Constrained multiobjective games in general topological spaces[J].Comput Math Appl,2000,39(3/4):23-30.
    [14] DING Xie-ping.Existence of Pareto equilibria for constrained multiobjective games in H-spaces[J].Comput Math Appl,2000,39(9):125-134.
    [15] DIGN Xie-ping, Park J Y, Jung I H. Pareto equilibria for constrained multiobjective games in locally L-convex spaces[J].Comput Math Appl,2003,46(10/11):1589-1599. doi: 10.1016/S0898-1221(03)90194-5
    [16] Yu H. Weak Pareto equilibria for multiobjective constrained games[J].Appl Math Lett,2003,16(5):773-776. doi: 10.1016/S0893-9659(03)00081-8
    [17] Lin Z, Yu J.The existence of solutions for the system of generalized vector quasi-equilibrium problems[J].Appl Math Lett,2005,18(4):415-422. doi: 10.1016/j.aml.2004.07.023
    [18] Lin L J, Cheng S F.Nash-type equilibrium theorems and competitive Nash-type equilibrium theorems[J].Comput Math Appl,2002,44(10/11):1369-1378. doi: 10.1016/S0898-1221(02)00263-8
    [19] DING Xie-ping.Weak Pareto equilibria for generalized constrained multiobjective games in locally FC-spaces[J].Nonlinear Anal,2006,65(3):538-545. doi: 10.1016/j.na.2005.09.029
    [20] DING Xie-ping.Collectively fixed point theorem in product locally FC-uniform spaces and applications[J].Nonlinear Anal,2007,66(11):2604-2617. doi: 10.1016/j.na.2006.03.043
    [21] Luc D T.Theory of Vector Optimization[M].Vol.319. Lecture Notes in Economics and Mathematical Systems.Berlin:Springer-Verlag,1989.
    [22] Lin L J, Yu Z T. 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
    [23] DING Xie-ping.Maximal element theorems in product FC-spaces and generalized games[J].J Math Anal Appl,2005,305(1):29-42. doi: 10.1016/j.jmaa.2004.10.060
    [24] Kelly J L.General Topology[M].Princeton,NJ:Van Nostrand, 1955.
    [25] Kthe G.Topological Vector Spaces Ⅰ[M].New York,Berlin:Springer-Verlag,1983,30.
    [26] Horvath C. Contractibility and general convexity[J].J Math Anal Appl,1991,156(2):341-357. doi: 10.1016/0022-247X(91)90402-L
    [27] 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
    [28] Park S.Fixed point theorems in locally G-convex spaces[J].Nonlinear Anal,2002,48(6):869-879. doi: 10.1016/S0362-546X(00)00220-0
    [29] DING Xie-ping.System of generalized vector quasi-equilibrium problems in locally FC-spaces[J].Acta Math Sinica,2006,22(5):1528-1538.
    [30] DING Xie-ping,Liou Y C, Yao J C.Generalized R-KKM type theorems in topological spaces with applications[J].Appl Math Lett,2005,18(12):1345-1350. doi: 10.1016/j.aml.2005.02.022
    [31] DING Xie-ping.Continuous selection, collectively fixed points and system of coincidence theorems in product topological spaces[J].Acta Math Sinica,2006,22(6):1629-1638. doi: 10.1007/s10114-005-0831-y
    [32] Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York:Wiley,1984.
    [33] Fan Ky. Fixed points and minimax theorems in locally convex spaces[J]. Proc Nat Acad Sci USA,1952,38(1):121-126. doi: 10.1073/pnas.38.2.121
  • 加载中
计量
  • 文章访问数:  2700
  • HTML全文浏览量:  107
  • PDF下载量:  790
  • 被引次数: 0
出版历程
  • 收稿日期:  2007-01-06
  • 修回日期:  2008-01-16
  • 刊出日期:  2008-03-15

目录

    /

    返回文章
    返回