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

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

Hongwei Jiao1 , Yunrui Guo1 and Fenghui Wang3

1Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China
 3Department of Mathematics, Luoyang Normal University, Luoyang 471022, China

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.