Articles

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

  • Chunyan LIU ,
  • Zihou ZHANG ,
  • Yu ZHOU
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  • School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China

Received date: 2016-10-28

  Online published: 2018-04-25

Supported by

Zihou Zhang is supported by the National Natural Science Foundation of China (11671252); Yu Zhou is supported by the National Natural Science Foundation of China (11771278).

Abstract

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.

Cite this article

Chunyan LIU , Zihou ZHANG , Yu ZHOU . A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2018 , 38(2) : 643 -650 . DOI: 10.1016/S0252-9602(18)30771-9

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