Modulus of Convexity, the Coeffcient $R(1,X)$, and Normal Structure in Banach Spaces
Hongwei Jiao, Yunrui Guo, and Fenghui Wang
Source: Abstr. Appl. Anal. Volume 2008 (2008), 5 pages.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aaa/1220969174
Digital Object Identifier: doi:10.1155/2008/135873
Zentralblatt MATH identifier:
05313192
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Abstract and Applied Analysis
