Banach空间中的kUKK性质  

kUKK Property in Banach Spaces

作　　者：樊丽颖 宋婧婧 张佳宁 Fan Liying;Song Jingjing;Zhang Jianing(Department of Mathematics, Harbin University of Science and Technology,Harbin 150080;Chongqing Institute of Engineering,Chongqing 400056)

机构地区：[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

出　　处：《数学物理学报（A辑）》2019年第4期705-712,共8页Acta Mathematica Scientia

基　　金：黑龙江省教育厅科技项目(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.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.

关 键 词：kUKK性质 几何常数 不动点性质 BANACH空间 

分 类 号：O177[理学—数学]