[1]赵亮,王微微,张兴.Banach空间具有正规结构的判定条件[J].哈尔滨理工大学学报,2018,(04):140-144.[doi:10.15938/j.jhust.2018.04.026]
 ZHAO Liang,WANG Wei wei,ZHANG Xing. Generalized Modulus of Smoothness in Banach Spaces[J].哈尔滨理工大学学报,2018,(04):140-144.[doi:10.15938/j.jhust.2018.04.026]
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Banach空间具有正规结构的判定条件
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《哈尔滨理工大学学报》[ISSN:1007-2683/CN:23-1404/N]

卷:
期数:
2018年04期
页码:
140-144
栏目:
管理科学与工程
出版日期:
2018-08-25

文章信息/Info

Title:
 Generalized Modulus of Smoothness in Banach Spaces
作者:
赵亮王微微张兴
哈尔滨理工大学 应用科学学院,黑龙江 哈尔滨 150080
Author(s):
 ZHAO LiangWANG WeiweiZHANG Xing
School of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China
关键词:
关键词:一致光滑广义光滑模Lindenstrauss公式正规结构
Keywords:
Keywords:uniform smoothness generalized modulus of smoothness lindenstrauss formula normal structure
分类号:
O1777
DOI:
10.15938/j.jhust.2018.04.026
文献标志码:
A
摘要:
摘要:为了研究Banach空间的几何常数,依据凸性模和光滑模的定义和性质,采用将光滑模推广到广义光滑模的方法来研究新常数。依据Lindenstrauss公式以及凸性模与光滑模的对偶关系,进一步研究广义光滑模与广义凸性模的的关系,不再局限于光滑模定义的条件,对新常数中的变量研究能够得出Banach空间具有的性质,从而给出了广义光滑模与广义凸性特征的一个关系,再通过广义光滑模与弱正交系数的关系,运用范数三角不等式,得出了Banach空间具有正规结构的充分条件。
Abstract:
Abstract:In order to study the geometric constants of Banach space, a new method is extended to study new constants by means of extending the modulus of smoothness to the generalized smooth mode On the basis of the Lindenstrauss formula and the duality between the modulus of convexity and modulus of smoothness, further study of generalized modulus of smoothness and generalized modulus of convexity and modulus of smoothness is no longer confined to the defined conditions, properties of the variables can be obtained in constant research of new space with Banach, which gives a relation between the generalized modulus of smoothness and generalized convex the characteristics. Through the relationship between generalized modulus of smoothness and weak orthogonal coefficients, by means of the norm of the triangle inequality, sufficient conditions are obtained for normal structure in Banach space
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参考文献/References:

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备注/Memo

备注/Memo:
基金项目:国家自然科学基金(11571085);黑龙江省教育厅科学技术研究项目(12541145)
更新日期/Last Update: 2018-10-25