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

G-凸空间内新的聚合不动点定理及应用

丁协平 朴忠烈

丁协平, 朴忠烈. G-凸空间内新的聚合不动点定理及应用[J]. 应用数学和力学, 2002, 23(11): 1101-1112.
引用本文: 丁协平, 朴忠烈. G-凸空间内新的聚合不动点定理及应用[J]. 应用数学和力学, 2002, 23(11): 1101-1112.
DING Xie-ping, Park Jong-yeoul. New Collectively Fixed Point Theorems and Applications in G-Convex Spaces[J]. Applied Mathematics and Mechanics, 2002, 23(11): 1101-1112.
Citation: DING Xie-ping, Park Jong-yeoul. New Collectively Fixed Point Theorems and Applications in G-Convex Spaces[J]. Applied Mathematics and Mechanics, 2002, 23(11): 1101-1112.

G-凸空间内新的聚合不动点定理及应用

基金项目: 国家自然科学基金资助项目(19871059);韩国工程科学基金和四川省教育厅重点科研基金资助项目([2000]25);韩国研究基金资助项目(1998-15-D00021)
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);朴忠烈(1945- ),男,韩国釜山人,教授.

  • 中图分类号: O177.92

New Collectively Fixed Point Theorems and Applications in G-Convex Spaces

  • 摘要: 由应用连续单位分解技巧和Tychonoff不动点定理对定义在非紧G-凸空间的乘积空间上的一族集值映象证明了一些新的不动点定理。作为应用,对G-凸空间的乘积空间的一簇子集证明了KyFan型非空交定理;在G-凸空间内给出了非线性不等式组解的一个存在定理和得到了一些抽象经济的平衡存在定理。这些定理改进和推广了很多最近文献中重要的已知结果。
  • [1] Tarafdar E. A fixed point theorem and equilibrium point of an abstract economy[J]. J Math Econom,1991,20(2):211-218.
    [2] LAN Kun-Quan, Webb J. New fixed point theorems for a family of mappings and applications to problems on sets with convex sections[J]. Proc Amer Math Soc,1998,126(4):1127-1132.
    [3] Ansari Q H, Yao J C. A fixed point theorem and its applications to a system of variational inequalities[J]. Bull Austral Math Soc,1999,59(2):433-442.
    [4] Singh S P, Tarafdar E, Watson B. A generalized fixed point theorem and equilibrium point of an abstract economy[J]. J Computat Appl Math,2000,113(1/2):65-71.
    [5] Tarafdar E. Fixed point theorems in H-spaces and equilibrium point of abstract economies[J]. J Austral Math Soc Ser A,1992,53(2):252-260.
    [6] CHANG Shi-sheng, Lee B S, Cho Y J, et al. On the generalized quasi-variational inequality problems[J]. J Math Anal Appl,1996,203(3):686-711.
    [7] LIN Lai-jiu, Park S. On some generalized quasi-equilibrium problems[J]. J Math Anal Appl,1998,224(1):167-181.
    [8] Patk S. Continuous selection theorems in generalized convex spaces[J]. Numer Funct Anal Optimiz,1999,20(5/6):567-583.
    [9] DING Xie-ping. New H-KKM theorems and their applications to geometric property, coincidence theorems, minimax inequality and maximal elements[J]. Indian J Pure Appl Math,1995,26(1):1-19.
    [10] DING Xie-ping. Gerenalized variational inequalities and equilibrium problems in generalized convex spaces[J]. Computera Math Applic,1999,38(7/8):180-197.
    [11] Wilansky A. Topology for Analysis[M]. Waltham Massachusetts: Ginn,1972.
    [12] Dugundji J. Topology[M]. Boston: Allyn and Bacon Inc,1966.
    [13] Husain T. Topology and Maps[M]. New York: Plenum Press,1977.
    [14] Kelley J L. General Topology[M]. Princeton:D Van Nostrand Co,1955.
    [15] Park S, Kim H. Coincidence theorems for admissible multifunctions on generalized convex spaces[J]. J Math Anal Appl,1997,197(1):173-187.
    [16] Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J]. J Math Anal Appl,1997,209(2):551-571.
    [17] Ben-El-Mechaiekh H, Chebbi S, Flornzano M, et al. Abstract convexity and fixed points[J]. J Math Anal Appl,1998,222(1):138-150.
    [18] Tychonoff A. Ein fixpunktsatz[J]. Math Ann,1935,111:767-776.
    [19] DING Xie-ping. Coincidence theorems in topological spaces and their applications[J]. Appl Math Lett,1999,12(7):99-105.
    [20] Tarafdar E. A fixed point theorem equivalent to the Fan-Knastre-Kuratowski-Mazurkiewicz theorem[J]. J Math Anal Appl,1987,128(3):475-479.
    [21] Shih M H, Tan K K. Non-compact sets with convex sections[J]. Pacific J Math,1985,119(2):473-479.
    [22] Fan Ky. Some properties of convex sets related fixed point theorems[J]. Math Ann,1984,266(3):519-527.
    [23] Ma T W. On sets with convex sections[J]. J Math Anal Appl,1964,27(2):413-416.
    [24] Fan Ky. Applications of a theorem concerning sets with convex sections[J]. Math Ann,1966,163(2):189-203.
    [25] DING Xie-ping, Kim W K, Tan K K. Equilibria of noncompact generalized games with L* majorized preference correspondences[J]. J Math Anal Appl,1992,164(3):508-517.
    [26] DING Xie-ping, Kim W K, Tan K K. A selection theorem and its application[J]. Bull Austral Math Soc,1992,46(2):205-212.
    [27] DING Xie-ping, Tan K K. On equilibria of noncompact generalized games[J]. J Math Anal Appl,1993,177(1):226-238.
  • 加载中
计量
  • 文章访问数:  2411
  • HTML全文浏览量:  98
  • PDF下载量:  649
  • 被引次数: 0
出版历程
  • 收稿日期:  2001-06-12
  • 修回日期:  2002-07-20
  • 刊出日期:  2002-11-15

目录

    /

    返回文章
    返回