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. 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 Zhang2,*()   

  1. 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:

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XkNUC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