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

Suyalatu Wulede, Shaoqiang Shang, Wurina Bao


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.


$k$ denting points, $k$ smooth spaces, $k$ very smooth spaces, $k$ strongly smooth spaces, Banach spaces

Subject classification

46B09; 46B20


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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