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| 局部凸空间的中点局部k-一致凸性与中点局部k-一致光滑性 | |
| 引用本文： | 陈利国,罗成,王君. 局部凸空间的中点局部k-一致凸性与中点局部k-一致光滑性[J]. 中山大学学报(自然科学版), 2013, 52(2): 52-56 |
| 作者姓名： | 陈利国 罗成 王君 |
| 作者单位： | 1. 内蒙古财经大学统计与数学学院,内蒙古 呼和浩特,010070 2. 内蒙古大学数学科学学院,内蒙古 呼和浩特,010021 |
| 基金项目： | 内蒙古自然科学基金资助项目 |
| 摘 要： | 引入局部凸空间的中点局部k-一致凸性和中点局部k-一致光滑性这一对对偶概念,它们既是Banach空间中点局部k-一致凸性和中点局部k-一致光滑性推广,又是局部凸空间中点局部一致凸性和中点局部一致光滑性的自然推广。讨论它们与其它k-凸性(k-光滑性)之间的关系。 |
| 关 键 词： | 偶对 中点局部k-一致凸性 中点局部k-一致光滑性 弱中点局部k-一致凸性 弱中点局部k-一致光滑性 |
| 收稿时间： | 2012-09-14; |
Midpoint Locally k-Uniformly Convexity and Midpoint Locally k-Uniformly Smoothness in Locally Convex Spaces |
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| CHEN Liguo , LUO Cheng , WANG Jun. Midpoint Locally k-Uniformly Convexity and Midpoint Locally k-Uniformly Smoothness in Locally Convex Spaces[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2013, 52(2): 52-56 | |
| Authors: | CHEN Liguo LUO Cheng WANG Jun |
| Affiliation: | (1. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China; 2. School of Mathematial Sciences, Inner Mongolia University, Hohhot 010021, China) |
| Abstract: | The dual notions of midpoint locally k-uniformly convexity and midpoint locally k-uniformly smooth on Locally Convex Spaces are introduced , which are generalizations of both midpoint locally k-uniformly convexity (midpoint locally k-uniformly smoothness) in Banach spaces and midpoint locally uniformly convexity (midpoint locally uniformly smoothness) in locally convex spaces. The relationship between them and the other convexity (smoothness) are discussed. |
| Keywords: | dual k-uniformly convexity')" href=" #" >midpoint locally k-uniformly convexity k-uniformly smoothness')" href=" #" >midpoint locally k-uniformly smoothness k-uniformly convexity')" href=" #" >weakly midpoint locally k-uniformly convexity k-uniformly smoothness')" href=" #" >weakly midpoint locally k-uniformly smoothness |
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