| 紧－凸性与紧－光滑性 |
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| 引用本文： | 郑喜印.紧－凸性与紧－光滑性[J].数学进展,1995(4). |
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| 作者姓名： | 郑喜印 |
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| 作者单位： | 云南大学数学系 |
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| 摘 要： | 本文首先通过暴露集和暴露泛函的概念引入了闭凸集的紧－严格凸、紧－强凸、紧－一致凸及紧－非常凸等概念。并用对偶映射给出了Ｂａｎａｃｈ空间的两种新光滑性—紧－一致光滑与紧－非常光滑。然后特别研究了Ｂａｎａｃｈ空间的紧－非常凸与紧－非常光滑。此外还得到关于对偶映射的两个新结果。
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| 关 键 词： | 暴露集 暴露泛函 紧－严格（强、一致、非常）凸 对偶映射 紧光滑性 |
Compact Convexity and Compact Smoothness |
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| Zheng Xiyin.Compact Convexity and Compact Smoothness[J].Advances in Mathematics,1995(4). |
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| Authors: | Zheng Xiyin |
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| Abstract: | By means of the concept of exposed set and exposed functional, several weintroduce the notion of the compact convexity of closed convex sets in Banach spaces,suchas compactly strict,strong , uniform and the very convexity,are introducted,Using the dualitymapping;the notions of compactly uniform and the very smoothness of Banach spaces are given.we study various compact convexity and smoothness of Banach spaces are studied,and two newresults relat ed to the duality mapping are obtained. |
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| Keywords: | exposed set exposed functiond compactly strict(strong uniform the very)convexity duality mapping compactly the very smoothness |
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