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

Hongwei Jiao, Yunrui Guo and Fenghui Wang

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

Abstract: Let δX(ϵ) 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 2δX(1 + ϵ) > max{(R(1, x) − 1)ϵ, 1 − (1 − ϵ/R(1, X) − 1)} for some ϵ ∈ [0, 1] which generalizes the known result by Gao and Prus.

Date: 2008
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https://doi.org/10.1155/2008/135873

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:135873

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