k-super-strongly convex and k-super-strongly smooth Banach spaces |
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Authors: | Suyalatu |
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Affiliation: | Department of Mathematics, Inner Mongolia Normal University, Huhhot 010022, PR China |
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Abstract: | In this paper, we introduce two types of new Banach spaces: k-super-strongly convex spaces and k-super-strongly smooth spaces. It is proved that these two notions are dual. We also prove that the class of k-super-strongly convexifiable spaces is strictly between locally k-uniformly rotund spaces and k-strongly convex spaces, and obtain some necessary and sufficient conditions of k-super-strongly convex space (respectively k-super-strongly smooth space). Also, for each k?2, it is shown that there exists a k-super-strongly convex (respectively k-super-strongly smooth) space which is not (k−1)-super-strongly convex (respectively (k−1)-super-strongly smooth) space. |
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Keywords: | k-super-strongly convex space k-super-strongly smooth space Banach space |
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