| n-Banach空间中的凸性研究 |
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| 引用本文： | 樊增平.n-Banach空间中的凸性研究[J].集宁师专学报,2008,30(4):7-12. |
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| 作者姓名： | 樊增平 |
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| 作者单位： | 内蒙古师范大学数学科学学院,内蒙古呼和浩特,010022 |
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| 摘 要： | 1985年，阎革兴（文1]）把Gahkr的2-赋范空间的概念推广得到了n-赋范空间，进而定义了n-Banach空间。讨论了n-Banach空间中的性质．同年，阎革兴在文2]中将严格凸与光滑性引入到了n-赋范空间中，而且得到了二者的关系定理．本文的主要目的是将一般Banach空间中的一致凸，局部一政凸，中点局部一致凸，强凸等概念推广到n—Banach空间中，并证明了几种凸性间的关系定理．
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| 关 键 词： | n-Banach空间 有界线性 n-泛函 一致凸 局部一致凸 强凸 |
The Research of Convexity in n-Banach Spaces |
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| FAN Zengping.The Research of Convexity in n-Banach Spaces[J].Journal of Jining Teachers College,2008,30(4):7-12. |
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| Authors: | FAN Zengping |
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| Institution: | FAN Zengping( Mathematics Science college, Inner Mongolia Normal University, Huhhot 010022, China) |
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| Abstract: | In this paper,the conceptions of uniformly convex,locally uniformly convex,strongly convex and so on are introduced to n-Banach spaces.Those are the generalization of Banach spaces'conceptions.In addition,it is shown that the relations of those conceptions in n-Banach spaces. |
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| Keywords: | n-Banach spaces bounded linearn-functional uniformly convex locally uniformly convex strongly convex |
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