| K-弱凸性与K-弱光滑性 |
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| 引用本文： | 黎永锦,舒小保.K-弱凸性与K-弱光滑性[J].中山大学学报(自然科学版),2002,41(5):8-10. |
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| 作者姓名： | 黎永锦 舒小保 |
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| 作者单位： | 中山大学数学与计算科学学院,广东,广州,510275 |
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| 摘 要： | 提出了K_弱凸性与K_弱光滑性 ,作为K_强凸性与K_强光滑性的推广 ,然后证明了K_弱凸性与K_弱光滑性是对偶性质 ;Banach空间X是非常凸的当且仅当X是严格凸的且K_弱凸的 ;Banach空间X是局部一致凸的当且仅当X是K_强凸的和严格凸的且具有 (WM)性质。
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| 关 键 词： | K-弱凸性 K-弱光滑性 K-弱暴露点 (WM)性质 |
| 文章编号： | 0529-6579(2002)05-0008-03 |
K-Weakly Convex and K-Weakly Smooth |
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| LI Yong_jin,SHU Xiao_bao.K-Weakly Convex and K-Weakly Smooth[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2002,41(5):8-10. |
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| Authors: | LI Yong_jin SHU Xiao_bao |
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| Abstract: | The \%K\%_weakly convex and \%K\%_weakly smooth are defined.It is shown that \%K\%_weakly convex and \%K\%_weakly smooth are dual notions, Banach space \%X\% is very convex if and only if \%X\% is strictly convex and \%K\%_weakly convex,and Banach space \%X\% is locally uniformly convex if and only if \%X\% is \%K\%_strongly convex, strictly convex, and \%X\% has property(WM). |
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| Keywords: | K\%_weakly convex \%K\%_weakly smooth \%K\%_weakly exposed point property(WM) |
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