SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES  

作　　者：Zihou ZHANG Yu ZHOU Chunyan LIU Jing ZHOU 张子厚;周宇;刘春燕;周晶(School of Mathematics Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China)

机构地区：[1]School of Mathematics Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China

出　　处：《Acta Mathematica Scientia》2022年第4期1621-1630,共10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 paper,we discuss the relation between τ-strongly Chebyshev,approximatively τ-compact k-Chebyshev,approximatively τ-compact,τ-strongly proximinal and proximinal sets,where τ is the norm or the weak topology.We give some equivalent conditions regarding the above proximinality.Furthermore,we also propose the necessary and sufficient conditions that a half-space is τ-strongly proximinal,approximatively τ-compact and τ-strongly Chebyshev.

关 键 词：Approximativeτ-compactness τ-strong proximinality proximinality Chebyshev set nearly strong convexity k-strong convexity k-strict convexity nearly strict convexity 

分 类 号：O177.2[理学—数学]