拓扑空间中的弱R-KKM映射—交定理和极大极小不等式

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

邓磊¹,
杨明歌^1,2

1.
西南大学数学与统计学院,重庆 400715;2.洛阳师范学院数学科学学院,洛阳 471022

基金项目: 国家自然科学基金资助项目(10471113);重庆市科委自然科学基金资助项目(CSTC,2005BB2097)

详细信息

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
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- 被引次数: 0
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

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

DENG Lei¹,
YANG Ming-ge^1,2

1.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China;

摘要

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．
- 弱R-KKM映射 /
- R-凸 /
- R-β-拟凸 /
- 广义R-KKM映射
Abstract: The concepts of weakly R-KKM mappings, R-convex and R-β-quasiconvex in general topological spaces without any convex structure are introduced. Relating to these, an extension to general topological spaces of Fan's matching theorem is obtained, namely Lemma 1.2. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. The results generalize and improve the corresponding results in the literature.
- weakly R-KKM mapping /
- R-convex /
- R-β-quasiconvex /
- generalized R-KKM mapping

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参考文献(12)

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