| 局部凸空间的k-一致极凸性与k-一致极光滑性 |
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| 引用本文： | 陈利国,罗成.局部凸空间的k-一致极凸性与k-一致极光滑性[J].数学的实践与认识,2011,41(20). |
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| 作者姓名： | 陈利国 罗成 |
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| 作者单位： | 1. 内蒙古财经学院统计与数学学院,内蒙古呼和浩特,010051
2. 内蒙古大学数学科学学院,内蒙古呼和浩特,010021 |
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| 基金项目： | 内蒙古教育厅项目(NJ09138); 内蒙古财经学院校级项目(ky0960) |
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| 摘 要： | 首先引入局部凸空间的k-一致极凸性和k-一致极光滑性这一对对偶概念,它们既是Banach空间k-一致极凸性和k-一致极光滑性推广,又是局部凸空间一致极凸性和一致极光滑性的自然推广.其次讨论它们与其它k-凸性(k-光滑性)之间的关系.最后,在P-自反的条件下给出它们之间的等价对偶定理.
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| 关 键 词： | 偶对 κ-一致极凸性 κ-一致极光滑性 P-自反 |
k-Uniformly Extreme Convexity and k-Uniformly Extreme Smoothness In Locally Convex Spaces |
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| CHEN Li-guo,LUO Cheng.k-Uniformly Extreme Convexity and k-Uniformly Extreme Smoothness In Locally Convex Spaces[J].Mathematics in Practice and Theory,2011,41(20). |
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| Authors: | CHEN Li-guo LUO Cheng |
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| Institution: | CHEN Li-guo~1,LUO Cheng~2 (1.School of Statistics and Mathematics,Inner Mongolia Finance and Economics College,Hohhot 010051,China) (2.School of Mathematial Sciences,Inner Mongolia University,Hohhot 010021,China) |
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| Abstract: | The dual notions of k-uniformly extreme convexity and k-uniformly extreme smoothness are introduced In locally convex spaces,which are generalization of both k-uniformly extreme convexity(k-uniformly extreme smoothness) in Banach spaces and uniformly extreme convexity(uniformly extreme smoothness) In locally convex spaces.The relationship between them and the other convexity(smoothness) are discussed.In addition, on the conditions of P-reflexivity,we obtain further the equivalent dual theorem of between k-u... |
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| Keywords: | dual k-uniformly extreme convexity k-uniformly extreme smoothness Preflexivity |
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