| 若干K凸性的等价条件 |
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| 引用本文： | 黎永锦,冼军.若干K凸性的等价条件[J].中山大学学报(自然科学版),2003,42(1):12-15,19. |
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| 作者姓名： | 黎永锦 冼军 |
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| 作者单位： | 中山大学数学系,广东,广州,510275 |
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| 摘 要： | 就一些K凸性的等价条件作了讨论，证明了几种K凸性在某种条件下是等价的，如当空间X是自反的且X和X*均有（H）性质时，则有7种K凸性等价，当空间X自反且有（H）性质，则有6种K凸性等价。
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| 关 键 词： | K－很凸 K－极凸 弱中点局部K－一致凸局部K－一致凸 K－强凸 K－严格凸 |
| 文章编号： | 0529-6579(2003)01-0012-05 |
Equivalence Conditions for Some K-Convexities |
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| XIAN Jun,LI Yong-jin.Equivalence Conditions for Some K-Convexities[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2003,42(1):12-15,19. |
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| Authors: | XIAN Jun LI Yong-jin |
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| Abstract: | The equivalence conditions for some K-convexities are explored, and obtain some conditions on which some K-convexities are equivalent to each other are obtained. For example, there are seven K- convexities equivalent to each other if Banach space X is reflexive and X, X* both possess (H) property respectively. If X is a reflexive space and has (H) property, then there are six K-convexities equivalent to each other. |
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| Keywords: | K-very convex K-strongly convex weak local mid-point K-uniformly convex K-extremely convex K-strictly convex |
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