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一般化凸空间上极大元和平衡点的存在问题 被引量：1

Existence problem of maximal element and equilibrium point on generalized convex spaces
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摘要 介绍了一般化凸空间上的Ψ*-凝聚映射的定义,并给出了它的一些性质和不动点定理,最后作为它们的应用,讨论了极大元存在问题和在抽象经济系统中的平衡点的存在问题. The definition of Ψ^＊- condensing map on generalized convex spaces was introduced, and its some properties and fixed point theorems were given, finally existence problems of maximal element and existence problem of equilibrium point in abstract economy system were discussed as their applications.
作者 朴勇杰
机构地区 延边大学理学院数学系
出处 《东北师大学报（自然科学版）》 CAS CSCD 北大核心 2008年第4期24-27,共4页 Journal of Northeast Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(10361005) 延边大学自然科学基金资助项目(2008)
关键词 一般化凸空间 不动点 Ψ^＊-凝聚映射 极大元 平衡点 generalized convex spaces fixed point Ψ^＊- condensing map maximal element equilibrium point
分类号 O189.1 [理学—基础数学] O177.91 [理学—基础数学]
  • 相关文献

参考文献8

  • 1朴勇杰,金光植.一般化凸空间上变分不等式解的存在定理[J].东北师大学报（自然科学版）,2007,39(1):28-31. 被引量：5
  • 2PARK SEHIE. New susclasses of generalized concex spaees[J ]. Fixed Point Theory and Applications, 2000 (2) :91-98.
  • 3LASSONDE M. On the use of KKM multimaps in fixed point theory and related topics[J]. J Math Anal Appl, 1983,97:151-201.
  • 4HORVATH C D. Contractility and generalized convexity[J ]. J Math Anal Appl, 1991,156:341-357.
  • 5朴勇杰,崔海兰.一般化凸空间的一些基本性质[J].延边大学学报（自然科学版）,2002,28(3):157-159. 被引量：4
  • 6METHA G S,TAN K-K,YUAN X Z. Fixed points,maximal elements and equilibia of generalized games[J]. Nonlinear Anal Theory, Method and Appl, 1997,28: 689-699.
  • 7SOUHAIL CHEBBI, MONIQUE FLORENZANO. Maximal dements and equilibria for condensing oorrespondences[J ]. Nonlinear Anal, 1999,38 : 995-1002.
  • 8YUAN X Z,TARAFDAR E. Maximal elements and eqilibria of generalized games for condensing correspondences[ J ]. J Math Anal Appl, 1996,203:13-30.

二级参考文献15

  • 1朴勇杰,金雪莲.一般化凸空间上ψ^＊-凝聚映射的不动点定理[J].东北师大学报（自然科学版）,2005,37(4):7-10. 被引量：1
  • 2[1]Park Sehie. New Subclasses of Generalized Concex Spaces[J]. Fixed Point Theory and Applications (Y J Cho, ed. ), Nova Sci Publ, New-York, 2000. 91 - 98.
  • 3[2]Lassonde M. On the Use of KKM Multimaps in Fixed Point Theory and Related Topics[J]. J Math Anal Appl, 1983,97:151 - 201.
  • 4[3]Horvath C D. Contractibility and Generalized Convexity[J]. J Math Anal Appl, 1991,156:341 - 357.
  • 5[4]Tan K K, Zhang X L. Fixed Point Theorems on G- convex Spaces and Applications[J]. Nonlinear Funct Anal Appl, 1996, (1) :1 - 19.
  • 6[5]Kim W K. Some Applications of Kakutani Fixed Point Theorem[J]. J Math Anal Appl, 1987,121:119 - 122.
  • 7[6]Shih M H, Tan K K. Covering Theorems of Convex Sets Related to Fixed Point Theorems[J]. Nonlinear and Convex Analysis(Proc. in honor of Ky Fan), Marcaldekker Inc, New-York and Basel,1987. 235-244.
  • 8[7]Park Sehie, Lee W B. A Unified Approach to Generalized KKM Maps in Generalized Convex Spaces[J]. J Nonlinear and Convex Anal, 2001,2.
  • 9[8]Park Sehie. Elements of the KKM Theory for Generalized Convex Spaces [ J ] Korean J Comp Appl Math, 2000,7:1 - 28.
  • 10SEHIE PARK.New subclasses of generalizded convex spaces[A].Fixed point theory and Applications (Y J Cho,ed)[C].New York:Nova Sci Publ,2000:91-99.

共引文献7

同被引文献11

  • 1朴勇杰,金光植.一般化凸空间上变分不等式解的存在定理[J].东北师大学报（自然科学版）,2007,39(1):28-31. 被引量：5
  • 2UDRISTE,CONSTANTIN. Convex functions and optimization methods on riemannian manifolds[M]. Kluwer:Academic Publishers, 1994 :65-102.
  • 3DANIEL AZAGRA,JUAN FERRERA. Fernando Lopez-Mesas,nonsmooth analysis and Hamilton Jacobi equations on smooth manifolds[J]. Joural of Functional Analysis, 2005,220 : 304-361.
  • 4LEDYAEV Y S,ZHU Q J. Techniques for nonsmooth analysis on smooth manifolds I: local problems[J]. Lecture Notes in Control and Information Sciences,2004(301):283-297.
  • 5LEDYAEV Y S, ZHU Q J. Techniques for nonsmooth analysis on smooth manifolds Ⅱ : deformations and flows[J]. Lecture Notes in Control and Information Sciences, 2004( 301 ):299-311.
  • 6DANIEL AZAGRA,JUAN FERRERA. Proximal calculus on riemannian manifolds[J]. Mediterranean Journal of Mathematics, 2005,2:437-450.
  • 7CLARKE F H, LEDYAEV Y S, STENN R J, et al. Nonsmooth analysis and control theory, grad texts in math[M]. Berlin: Springer, 1998 : 69-96.
  • 8CLARKE F H. Optimization and nonsmooth analysis[M]. New York : John Wiley Sons, Inc, 1983 : 25-95.
  • 9BOOTH BY. An introduction to differential manifolds and riemannian geometry, second edition[M]. Orlando:Academic Press, 1988 :10-150.
  • 10MINAMI M. Weak pareto optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space[J]. JOTA,1983,41(3):451 -461.

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东北师大学报（自然科学版）
2008年 第4期

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