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2008 Modulus of Convexity, the Coeffcient R ( 1 , X ) , and Normal Structure in Banach Spaces
Hongwei Jiao, Yunrui Guo, Fenghui Wang
Abstr. Appl. Anal. 2008: 1-5 (2008). DOI: 10.1155/2008/135873

Abstract

Let δ X ( 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 2 δ X ( 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.

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Hongwei Jiao. Yunrui Guo. Fenghui Wang. "Modulus of Convexity, the Coeffcient R ( 1 , X ) , and Normal Structure in Banach Spaces." Abstr. Appl. Anal. 2008 1 - 5, 2008. https://doi.org/10.1155/2008/135873

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1166.46302
MathSciNet: MR2411041
Digital Object Identifier: 10.1155/2008/135873

Rights: Copyright © 2008 Hindawi

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