Banach空间中的kUKK性质

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 705-712.

• 论文 • 下一篇

Banach空间中的kUKK性质

樊丽颖¹(),宋婧婧¹(),张佳宁^2,*()

¹ 哈尔滨理工大学理学院哈尔滨 150080
² 重庆工程学院重庆 400056

收稿日期:2018-03-22 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 张佳宁 E-mail:fan_liying@163.com;804582993@qq.com;2536754451@qq.com
作者简介:樊丽颖, E-mail:fan_liying@163.com|宋婧婧, E-mail:804582993@qq.com
基金资助:
黑龙江省教育厅科技项目(12541161)

kUKK Property in Banach Spaces

Liying Fan¹(),Jingjing Song¹(),Jianing Zhang^2,*()

¹ Department of Mathematics, Harbin University of Science and Technology, Harbin 150080
² Chongqing Institute of Engineering, Chongqing 400056

Received:2018-03-22 Online:2019-08-26 Published:2019-09-11
Contact: Jianing Zhang E-mail:fan_liying@163.com;804582993@qq.com;2536754451@qq.com
Supported by:
the Science and Technology Project of Heilongjiang Provincial Department of Education(12541161)

摘要/Abstract

摘要：

给出Banach空间X的一个新的几何性质-kUKK，证明了具有该性质的Banach空间X具有弱Banach-Saks性质；Banach空间X是kNUC的充分必要条件是自反且具有kUKK性质；鉴于几何常数在Banach空间几何性质中扮演的重要角色，由kUKK的定义给出了新常数R₂(X)的定义，并证明了当R₂(X)< k时，Banach空间X具有弱不动点性质；最后计算R₂(X)在Cesaro序列空间中的具体值.

关键词: kUKK性质, 几何常数, 不动点性质, Banach空间

Abstract:

A new geometric property of Banach space kUKK is given, It is proved that Banach space with this property has weak Banach-saks property, Banach space X is kNUC if and only if it is reflexive and has kUKK property. considering the important role of geometric constants in Banach space geometric properties, The definition of the new constant R₂(X) < k is given by the definition of kUKK and proved that when R₂(X)< k, the Banach space X has a weak fixed point property. Finally, the specific values are calculated in the Cesaro sequence space.

Key words: kUKK Property, Geometric Constant, Fixed Point Property, Banach Space

中图分类号:

O177

樊丽颖,宋婧婧,张佳宁. Banach空间中的kUKK性质[J]. 数学物理学报, 2019, 39(4): 705-712.

Liying Fan,Jingjing Song,Jianing Zhang. kUKK Property in Banach Spaces[J]. Acta mathematica scientia,Series A, 2019, 39(4): 705-712.

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Banach空间中的kUKK性质

kUKK Property in Banach Spaces

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