Abstract and Applied Analysis
Volume 2008 (2008), Article ID 135873, 5 pages
doi:10.1155/2008/135873
Research Article

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

Hongwei Jiao,1 Yunrui Guo,1 and Fenghui Wang2

1Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China
2Department of Mathematics, Luoyang Normal University, Luoyang 471022, China

Received 7 April 2008; Accepted 27 May 2008

Academic Editor: William A. Kirk

Copyright © 2008 Hongwei Jiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.