| 广义凸空间内的KKM型定理和极小极大不等式及鞍点定理 |
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| 引用本文： | 丁协平.广义凸空间内的KKM型定理和极小极大不等式及鞍点定理[J].数学学报,2004,47(4):711-722. |
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| 作者姓名： | 丁协平 |
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| 作者单位： | 四川师范大学数学与软件科学学院,成都,610066 |
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| 基金项目： | 国家自然科学基金(19871059)，四川省教育厅重点研究基金 |
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| 摘 要： | 本文在非紧G-凸空间内对具有有限闭值和有限开值的G-KKM,广义G-KKM和广义S-KKM映象建立了某些新的KKM型定理。应用这些KKM型定理,在G-凸空间内得到了新的 Ky Fan型极小极大不等式和鞍点定理。这些结论推广了最近文献中的许多已有结果。
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| 关 键 词： | G-KKM型定理 极小极大不等式 鞍点 |
| 文章编号： | 0583-1431(2004)04-0711-12 |
KKM Type Theorems and Minimax Inequalities and Saddle Point Theorems in Generalized Convex Spaces |
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| Xie Ping DING College of Mathematics and Software Science,Sichuan Normal University Chengdu ,P. R. China.KKM Type Theorems and Minimax Inequalities and Saddle Point Theorems in Generalized Convex Spaces[J].Acta Mathematica Sinica,2004,47(4):711-722. |
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| Authors: | Xie Ping DING College of Mathematics and Software Science Sichuan Normal University Chengdu P R China |
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| Institution: | Xie Ping DING College of Mathematics and Software Science, Sichuan Normal University Chengdu 610066, P. R. China |
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| Abstract: | In this paper, some new generalized KKM type theorems for G-KKM, gener-
alized G-KKM and generalized S-KKM mappings with finitely closed values and with
finitely open values are established in noncompact G-convex spaces. By using these
KKM type theorems, some new Ky Fan type minimax inequalities and saddle poiat
theorems are obtained in G-convex space. These results generalize a number of known
results in the recent literature. |
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| Keywords: | G-KKM type theorem Finitely closed-valued (open-valued) mapping Mini-max inequality Saddle point |
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