A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES  

作　　者：刘春燕 张子厚 周宇 

机构地区：[1]School of Mathematics Physics and Statistics, Shanghai University of Engineering Science

出　　处：《Acta Mathematica Scientia》2018年第2期643-650,共8页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11671252);supported by the National Natural Science Foundation of China(11771278)

摘　　要：In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.

关 键 词：k-Chebyshev set approximatively weak compactness approximative compactness weak midpoint locally k-uniform rotundity midpoint locally k-uniform rotundity k-strict rotundity 

分 类 号：O177.2[理学—数学]