| Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces |
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| 引用本文： | 邓磊,杨明歌.Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces[J].应用数学和力学(英文版),2007,28(1):103-109. |
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| 作者姓名： | 邓磊 杨明歌 |
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| 作者单位： | School of Mathematics and Statistics Southwest University Chongqing 400715 P. R. China，School of Mathematics and Statistics Southwest University Chongqing 400715 P. R. China，College of Mathematics Science Luoyang Normal University Luoyang 471022 Henan Province P. R. China |
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| 基金项目： | 国家自然科学基金;重庆市自然科学基金 |
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| 摘 要： | In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. 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. Our results generalize and improve the corresponding results in the literature.
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| 关 键 词： | R-β-quasiconvex |
| 收稿时间： | 2005-10-09 |
| 修稿时间： | 2006-10-31 |
Weakly <Emphasis Type="Italic">R</Emphasis>-KKM mappings—intersection theorems and minimax inequalities in topological spaces |
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| Deng Lei,Yang Ming-ge.Weakly R-KKM mappings—intersection theorems and minimax inequalities in topological spaces[J].Applied Mathematics and Mechanics(English Edition),2007,28(1):103-109. |
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| Authors: | Deng Lei Yang Ming-ge |
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| Institution: | 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China
2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China;College of Mathematics Science, Luoyang Normal University,Luoyang 471022, Henan Province, P. R. China |
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| Abstract: | In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general
topological spaces of Fan’s matching theorem, namely that Lemma 1.2 in this paper. 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. Our results generalize and improve the corresponding results in the literature.
Project supported by the National Natural Science Foundation of China (No.10471113) and the Natural Science Foundation of
Chongqing Municipal Commission of Science and Technology (No.2005BB2097) |
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| Keywords: | weakly R-KKM mapping R-convex generalized R-KKM mapping |
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