| MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE |
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| 作者姓名： | 郑喜印 温忠粦 |
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| 作者单位： | Zheng Xiyin; Wen Zhonglin (Department of Mathematics，Yunnan University，Kunming 650091，P. R. China)(Institute of Educational Science，South China Normal University，Guangzhou 510631，P. R. China) |
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| 摘 要： | I.IntroductionFanKyinequalityisaveryusefultoolinnoolinearanalysiswhichasserts:LetXbeanonemptycompactconvexsetinatopologicallinearspaceandWbeareal-valuedfunctiondefinedonXxX.Assumethat(i)9(x,y)islowersemicontinuousinac;(n)9(x,y)isquasiconcaveiny.ThenthereisboaXsuchthatsHPg(xo'Y)$sZPp(x,x).SinceFanKyprovedtheinequalityin1972,variousg...,.li..tlon,havebeen;v..byseveralauthors(seel-3]andreferencestherein).Thepreviousgeneralizationsallremainedtheconditions(i)-'9(x,y)beinglowersemicontinuous…
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| 收稿时间： | 10 November 1995 |
Minimax theorem and saddle point theorem without linear structure |
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| Zheng Xiying,Wen Zhonglin.MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE[J].Applied Mathematics and Mechanics(English Edition),1998,19(4):375-380. |
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| Authors: | Zheng Xiying Wen Zhonglin |
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| Institution: | (1) Department of Mathematics, Yunnan University, 650091 Kunming, P. R. China;(2) Institute of Educational Science, South China Normal University, 510631 Guangzhou, P. R. China |
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| Abstract: | In the paper ,a new kind of concavity of a function defined on a set without linear structure is introduced and a generalzation of Fan Ky ineqality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established. |
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| Keywords: | minimax theorem saddle point theorem topological space |
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