| 引用本文： |
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马百万,魏文展,张吉超.局部凸空间有限严格凸性和有限光滑性[J].广西科学,2012,19(2):112-114. [点击复制]
- MA Bai-wan,WEI Wen-zhan,ZHANG Ji-chao.Finite Strict Convexity and Finite Smoothness in Locally Convex Spaces[J].Guangxi Sciences,2012,19(2):112-114. [点击复制]
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| 摘要: |
| 引入局部凸空间有限严格凸和有限光滑性的概念,建立对偶关系,证明局部凸空间中(X⊕Y)1的有限严格凸和有限光滑性既是Banach空间有限严格凸和有限光滑性概念在局部凸空间中的推广,又是局部凸空间k-严格凸和k-光滑性的自然推广. |
| 关键词: 局部凸空间 k-严格凸 k-光滑性 有限严格凸性 有限光滑性 |
| DOI： |
| 投稿时间：2012-02-14 |
| 基金项目:广西自然科学基金项目(桂科自0728050)资助。 |
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| Finite Strict Convexity and Finite Smoothness in Locally Convex Spaces |
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MA Bai-wan1, WEI Wen-zhan2, ZHANG Ji-chao1
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| (1.Collge of Mathematical Science, Guangxi Teachers Education University, Nanning, Guangxi 530023, China;2.Guangxi Economic and Trade Polytechnic, Nanning, Guangxi, 530021, China) |
| Abstract: |
| The concept of finite strict convexity and finite smoothness space is introduced into locally convex space. It is shown that there exists a duality between finite strict convexity and finite smoothness, and some geometrical properties of quotient, finite strict convexity with (X⊕Y)1 and finite smoothness with (X⊕Y)1 are investigated in this thesis. |
| Key words: locally convex spaces k-strictly convexity k-smoothness finite strict convexity finite smoothness |
