K-uniformly rotund spaces andk-uni formly smooth spaces |
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| Authors: | Suyalatu Congxin Wu |
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| Institution: | (1) Department of Mathematics, Inner Mongolia Normal University, 010022 Huhhot, China;(2) Department of Mathematics, Harbin Institute of Technology, 150006 Harbin, China |
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| Abstract: | The conception ofk-uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that thek-uniform smoothness and Sullivan’sK-uniform rotundity (KUR) are the daul notions. X* is a KUR space if and only if X is a KUS space, X* is a KUS space if and
only if X is a KUR space. If X is a KUS space, then X is a (K + 1) US space. It is also proved that the KUS space includes
the Nan’sk-strongly smooth space. |
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| Keywords: | K-uniform smoothness K-uniform convexity |
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