| k-非常凸、k-非常光滑与(弱)中点局部k-一致光滑空间 |
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| 引用本文： | 陈利国,罗成.k-非常凸、k-非常光滑与(弱)中点局部k-一致光滑空间[J].内蒙古大学学报(自然科学版),2007,38(5):494-497. |
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| 作者姓名： | 陈利国 罗成 |
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| 作者单位： | 1. 内蒙古大学数学系,呼和浩特,010021;内蒙古财经学院基础部,呼和浩特,010051
2. 内蒙古大学数学系,呼和浩特,010021 |
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| 摘 要： | 引入推广的Banach空间的k-非常凸、k-非常光滑、(弱)中点局部k-一致光滑性的概念,讨论了它们与其它k-凸性(k-光滑性)之间的关系,证明k-非常凸性和k-非常光滑性具有对偶性质,(弱)中点局部k-一致光滑性与(弱)中点局部k-一致凸性具有对偶性质.
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| 关 键 词： | k-非常凸 k-非常光滑 (弱)中点局部k-一致凸 (弱)中点局部k-一致光滑 非常凸 非常光滑 中点局部 一致光滑空间 Convex Smooth Weakly 一致凸性 对偶性质 关系 一致光滑性 Banach |
| 文章编号： | 1000-1638（2007）05-0494-04 |
| 修稿时间： | 2006-05-22 |
k-Very Convex,k-Very Smooth and(Weakly) Midpoint Locally k-Uniformly Smooth Spaces |
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| CHEN Li-guo,LUO Cheng.k-Very Convex,k-Very Smooth and(Weakly) Midpoint Locally k-Uniformly Smooth Spaces[J].Acta Scientiarum Naturalium Universitatis Neimongol,2007,38(5):494-497. |
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| Authors: | CHEN Li-guo LUO Cheng |
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| Institution: | 1. Department of Mathematics, Inner Mongolia University, Hohhot 010021, China;2. Department of Basic Sciences, Inner Mongolia Finance and Economics College, Hohhot 01 0051, China |
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| Abstract: | The generalized notions of k-very convex,k-very smooth and(weakly) midpoint locally k-uniformly smooth are introduced respectively,and the relationship between them and the other kconvex(k-smooth) are discussed.It is proved that there are dual properties between k-very convex and k-very smooth,(weakly)midpoint locally k-uniformly convex and(weakly) midpoint locally k-uniformly smooth respectively. |
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| Keywords: | k-very convex k-very smooth (weakly) midpoint locally k-uniformly convex (weakly)midpoint locally k-uniformly smooth |
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