Korean J. Math. Vol. 24 No. 3 (2016) pp.397-407
DOI: https://doi.org/10.11568/kjm.2016.24.3.397

$k-$ denting points and $k-$ smoothness of Banach spaces

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Published: Sep 30, 2016
Keywords:
$k$ denting points, $k$ smooth spaces, $k$ very smooth spaces, $k$ strongly smooth spaces, Banach spaces
Mathematics Subject Classification:
46B09, 46B20

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Suyalatu Wulede
College of Mathematics Science Inner Mongolia Normal University Hohhot 010022,P.R.China
Shaoqiang Shang
School of Science Northeast Forestry University Harbin 150040,P.R.China
Wurina Bao
Xilingol Vacation College Xilinhot 026000,P.R.China

Abstract

In this paper, the concepts of $k-$smoothness, $k-$very smoothness and $k-$strongly smoothness of Banach spaces are dealt with together briefly by introducing three types $k-$denting point regarding different topology of conjugate spaces of Banach spaces. In addition, the characterization of first type $w^{\ast}-k$ denting point is described by using the slice of closed unit ball of conjugate spaces.


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Supporting Agencies

This work was supported by the National Natural Science Foundation of China (Grant no.11561053) and Foundation of Inner Mongolia Normal University RCPY-2-2012-K-034.

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