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4. Modulus of Convexity, the Coeffcient R(1,X), and Normal Structure in Banach Spaces

Author

Jiao, Hongwei, Guo, Yunrui, and Wang, Fenghui

Subjects
Article Subject, lcsh:Mathematics, lcsh:QA1-939
Abstract

Let ${\delta }_{\text{X}}(\epsilon )$ and $R(1,X)$ be the modulus of convexity and the Domínguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach space $X$ has normal structure if $2{\delta }_{X}(1+\epsilon )>\text{max}\{(R(1,x)-1)\epsilon ,1-(1-\epsilon /R(1,X)-1)\}$ for some $\epsilon \in [0,1]$ which generalizes the known result by Gao and Prus.

Published
2008

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