曹温淳.Banach空间上范数的各种k光滑性[J].数学研究及应用,1995,15(2):244~248 |
Banach空间上范数的各种k光滑性 |
Various k-Smoothnesses of Norms on Banach Spaces |
投稿时间:1992-06-27 修订日期:1993-04-04 |
DOI:10.3770/j.issn:1000-341X.1995.02.016 |
中文关键词: k很光滑 k光滑 弱Hahn-Banach光滑 RNP |
英文关键词:k-smoothness very k-smoothness Hahn-Banach smoothness. |
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中文摘要: |
本文中,作者提出了k很光滑的概念,并研究了它和k光滑,弱Hahn-Banach光滑以及RNP之间的关系;还讨论了k光滑性和k强光滑性(kSS)的一些等价条件。 |
英文摘要: |
We define a concept of very k-smoothness(kVS) for every natural number k, andgives the necessary and sufficient conditions for very k-smoothness to be k-smoothnessand weak Hahn-Banach smoothness (w (H-B)S).The results extend a conclusion of [3].Moreover, we give several equivalent conditions for k-smoothness, strong k-smoothness,uniform k-convexity, weak uniform k-convexity and weak uniform k-convexity. |
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