| 关于K极光滑空间 |
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| 引用本文： | 曾朝英,苏雅拉图.关于K极光滑空间[J].集宁师专学报,2010,32(4). |
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| 作者姓名： | 曾朝英 苏雅拉图 |
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| 作者单位： | 1. 集宁师范学院数学系,内蒙古,乌兰察布,012000
2. 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： | 2001年冼军引入了k极光滑空间的概念,作为与其对偶的想法苏雅拉图和李广利引入了k极凸空间,并充分地研究了这一类凸性空间.虽然k极光滑空间概念较早被提出来,但是这一类光滑性空间尚未得到深入的研究,甚至这一类光滑性与其它光滑性之间的关系尚未弄清楚,本文深入研究了这一类光滑性空间,得到了它的一些性质以及与其它光滑性质之间的关系.另外,证明了:若X是弱局部k一致凸空间,则对每个x∈S(X),f∈Sx是X*的k光滑点。
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| 关 键 词： | k极（非常极）光滑 k（非常）光滑 弱中点局部k一致光滑 弱局部k一致凸 |
On the k-Extremely Smooth Spaces |
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| Zeng Chaoying,Suyalatu.On the k-Extremely Smooth Spaces[J].Journal of Jining Teachers College,2010,32(4). |
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| Authors: | Zeng Chaoying Suyalatu |
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| Institution: | Zeng Chaoying1,Suyalatu2(1.Department of Mathematics,College of Jining,Wulanchabu,012000,China,2.College of Mathematics Science,Inner Mongolia Normal University,Huhhot,010022,China) |
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| Abstract: | In this paper,the k-extremely smooth spaces are studied deeply,and their properties and the relations with some known smooth spaces are discussed.It is proved that if X is a weakly locally k-uniformly convex space,then f ∈Sx is the k-smooth points of X* for any x ∈S(X). |
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| Keywords: | k-extremely(very extremely) smooth spaces k(very)smooth spaces weakly midpoint locally k-uniformly smooth spaces weakly locally k-uniformly convex spaces |
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