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抽象凸空间上类K的性质及聚合不动点定理

Properties of Class K and Collectively Fixed Point Theorems on Abstract Convex Spaces
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摘要 给出抽象凸空间上映射类K的两个性质,利用已知抽象凸空间上的重叠点定理讨论抽象凸空间上映射的不动点存在问题,得到了若干新的不动点定理,同时进一步给出了抽象凸空间族的乘积空间上映射族的聚合不动点定理. We first gave two properties of map class K on Abstract convex spaces,and then used the well-known coincidence point theorem on Abstract convex spaces to discuss the existence problem of fixed points for maps on Abstract convex spaces and obtained some new fixed point theorems,from which several collectively fixed point theorems were established for a family of maps on a product space of a family of Abstract convex spaces.
作者 朴勇杰 石仁淑 崔海兰
机构地区 延边大学理学院数学系 吉林市朝鲜族中学
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2012年第3期381-386,共6页 Journal of Jilin University:Science Edition
基金 吉林省教育厅"十二五"科学技术研究项目(批准号:吉教科合字[2011]第434号)
关键词 抽象凸空间 映射类K KC KO 聚合不动点定理 KKM映射 Abstract convex space map class K KC KO collectively fixed point theorem KKM map
分类号 O177.3 [理学—基础数学] O189.11 [理学—基础数学]
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参考文献12

  • 1Park S. On Generalization of the KKM Principle on Abstract Convex Space [J]. Nonlinear Anal Forum, 2006, 11 (1) : 67 -77.
  • 2TIAN Guo-qiang. Generalization of FKKM Theorem and the Ky Fan Minimax Inequality with Applications to Maximal Elements, Price Equilibrim, and Complementarity [J]. J Math Anal Appl, 1992, 170(2) : 457-471.
  • 3Lassonde M. On the Use of KKM Multifunctions in Fixed Point Theory and Related Topics [ J ]. J Math Anal Appl, 1983, 97(1) : 151-201.
  • 4Hovarth C. Contractibility and Generalized Convexity [J]. J Math Anal Appl, 1991, 156(2) : 341-357.
  • 5Park S, Kim H. Coincidence Theorems for Admissible Multifunctions on Generalized Convex Spaces [ J ]. J Math Anal Appl, 1996, 197(1): 173-187.
  • 6Kim H, Park S. Remarks on the KKM Property for Open Valued Muhimaps on Generalized Convex Spaces [ J ]. J Korean Math Soc, 2005, 42(1) : 101-110.
  • 7/ DING Xie-ping. Generalized KKM Type Theorems in FC-Spaces with Applications ( I ) [ J ]. J Glob Optim, 2006- / 36(4) : 581-596.
  • 8Park S. Fixed Point Theorems on -Maps in Abstract Convex Space [ J ]. Nonlinear Anal Forum, 2006, 11 (2) 117-127.
  • 9Park S. A Genesis of General KKM Theorems for Abstract Convex Spaces [J]. J Nonlinear Anal Optim, 2011, 2( 1 ) : 121-132.
  • 10Park S. The KKM, Matching, and Fixed Point Theorem in Generalized Convex Spaces [ J ]. Nonlinear Funct Anal & Appl, 2006, 11(1) : 130-154.

二级参考文献9

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吉林大学学报（理学版）
2012年 第3期

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