## 留言板

 引用本文: 邓磊, 杨明歌. 拓扑空间中的弱R-KKM映射—交定理和极大极小不等式[J]. 应用数学和力学, 2007, 28(1): 92-98.
DENG Lei, YANG Ming-ge. Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces[J]. Applied Mathematics and Mechanics, 2007, 28(1): 92-98.
 Citation: DENG Lei, YANG Ming-ge. Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces[J]. Applied Mathematics and Mechanics, 2007, 28(1): 92-98.

## 拓扑空间中的弱R-KKM映射—交定理和极大极小不等式

###### 作者简介:邓磊(1957- ),男,重庆市人,教授(联系人.Tel:+86-23-68388606;E-mail:denglei@swu.edu.cn).
• 中图分类号: O177.91

## Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces

• 摘要: 在不具有任何凸性结构的一般拓扑空间中引入弱R-KKM映射，R-凸和R-β-拟凸这些新的概念．将Ky Fan匹配定理推广到一般拓扑空间中，即该文的引理1.2．利用引理1.2，在一般拓扑空间中证明了两个交定理．利用交定理，在一般拓扑空间中证明了一些Ky Fan型极大极小不等式．该文的结果推广和改进了文献中的相关结果．
•  [1] Knaster B, Kuratowski C,Mazurkiewicz S.EinBeweis des fixpunktsatzes fur n-dimensionale simplexe[J].Fund Math,1929,14(1):132-137. [2] Fan K.A generalization of Tychonoff's fixed point theorem[J].Math Ann,1961,142(3):305-310. [3] Park S.Generalizations of Ky Fan's matching theorems and their applications[J].J Math Anal Appl,1989,141(1):164-176. [4] Chang T H,Yen C L. KKM property and fixed point theorems[J].J Math Anal Appl,1996,203(1):224-235. [5] Lin L J, Ko C J, Park S. Coincidence theorems for set-valued mapps with G-KKM property on generalized convex space[J].Discuss Math Differential Incl,1998,18(1):69-85. [6] Balaj M.Weakly G-KKM mappings, G-KKM property, and minimax inequalities[J].J Math Anal Appl,2004,294(1):237-245. [7] Deng L, Xia X. Generalized R-KKM theorems in topological spaces and their applicatons[J].J Math Anal Appl,2003,285(2):679-690. [8] Park S, Kim H. Admissible classes of multifunctions on generalized convex spaces[J].Proc Coll Natur Sci Seoul National University,1993,18(1):1-21. [9] Shih M H. Covering properties of convex sets[J].Bull London Math Soc,1986,18(1):57-59. [10] Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(2):551-571. [11] Park S. Fixed point theorems in locally G-convex spaces[J].Nonlinear Anal,2002,48(6):869-879. [12] Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York:Wiley,1984.

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##### 出版历程
• 收稿日期:  2005-10-09
• 修回日期:  2006-10-31
• 刊出日期:  2007-01-15

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