| 非紧集上不连续函数的Ky Fan不等式及其等价形式和应用 |
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| 引用本文： | 彭定涛.非紧集上不连续函数的Ky Fan不等式及其等价形式和应用[J].应用数学学报,2011,34(3). |
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| 作者姓名： | 彭定涛 |
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| 作者单位： | 北京交通大学理学院,北京100044;贵州大学理学院,贵阳550025 |
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| 基金项目： | 国家973计划，贵州省自然科学基金 |
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| 摘 要： | 证明了非紧集上不具有任何连续性的函数弱Ky Fan点的存在性,给出了在函数只具非常弱的连续性和凸性条件下非紧集上Ky Fan不等式解的存在性,并给出它的两种等价形式.作为应用:(1)得到Ky Fan截口定理和Fan-Browder不动点定理的推广;(2)应用于博弈理论,得到几个新的Nash平衡存在性定理.
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| 关 键 词： | Ky Fan不等式 存在性 截口定理 不动点定理 Nash平衡 |
Ky Fan's Inequalities for Discontinuous Functions on Non-compact Set and Its Equivalent Version with Their Applications |
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| PENG DINGTAO.Ky Fan's Inequalities for Discontinuous Functions on Non-compact Set and Its Equivalent Version with Their Applications[J].Acta Mathematicae Applicatae Sinica,2011,34(3). |
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| Authors: | PENG DINGTAO |
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| Institution: | PENG DINGTAO (School of Science,Beijing Jiaotong University,Beijing 100044) (School of Science,Guizhou University,Guizhou,Guiyang 550025) |
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| Abstract: | The existence of weakly Ky Fan's point for the functions with no continuity on the non-compact set is proved.Based on this result,the Ky Fan's inequality is generalized to the functions with weak continuity,weak convexity and without compactness of the set. Author also give two equivalent versions for the result.As applications,(1) Ky Fan's section theorem and Fan-Browders's fixed point theorem are generalized;(2) some new existence theorems of Nash equilibria for n-person non-cooperative games are proved. |
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| Keywords: | Ky Fan's inequality existence section theorem fixed point theorem Nash equilibrium |
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