| 局部凸空间中若干种k-凸性和k-光滑性的研究 |
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| 引用本文： | 郝建军,刘德.局部凸空间中若干种k-凸性和k-光滑性的研究[J].内蒙古大学学报(自然科学版),2010,41(1). |
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| 作者姓名： | 郝建军 刘德 |
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| 作者单位： | 内蒙古大学数学科学学院,呼和浩特,010021 |
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| 摘 要： | 利用k维凸体体积统一给出了局部凸空间中k-一致凸和k-一致光滑,k-局部一致凸和k-局部一致光滑等定义,证明了它们是赋范空间相应概念的推广,并指出了它们之间的蕴含关系以及在P-自反意义下的对偶关系.
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| 关 键 词： | 局部凸空间 k-凸性 k-光滑性 P-自反 对偶 |
Study on Some Kinds of k-Convexity and k-Smoothness in Locally Convex Spaces |
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| HAO Jian-jun,LIU De.Study on Some Kinds of k-Convexity and k-Smoothness in Locally Convex Spaces[J].Acta Scientiarum Naturalium Universitatis Neimongol,2010,41(1). |
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| Authors: | HAO Jian-jun LIU De |
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| Institution: | School of Mathematics/a>;Inner Mongolia University/a>;Hohhot 010021/a>;China |
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| Abstract: | The definitions of k-uniformly convex,locally k-uniformly convex,k-uniformly smooth,locally k-uniformly smooth,etc.in locally convex spaces are given by k-dimension convex volume.It is proved that they are the extension of corresponding concepts in normed spaces.Their deduce and dual relationship are also discussed in the case of P-reflexivity. |
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| Keywords: | locally convex space k-convexity k-smoothness P-reflexivity dual |
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