Modulus of Convexity, the Coeffcient R(1, X), and Normal Structure in Banach Spaces
Hongwei Jiao, Yunrui Guo, Fenghui Wang · Abstract and Applied Analysis · 2008
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.