Banas-Hajnosz-Wedrychowicz type modulus of convexity and normal structure in Banach spaces
type: Item
instance of: scholarly article
title: Banas-Hajnosz-Wedrychowicz type modulus of convexity and normal structure in Banach spaces
zbMATH Open document ID: 1407.46014
published in: Journal of Fixed Point Theory and Applications
publication date: 2018-07-18T00:00:00Z
review text: The author presents some sufficient conditions for a Banach space to have uniform normal structure in terms of inequalities involving the coefficients \(SY_X(\varepsilon)\) defined by \textit{S. Saejung} and \textit{J. Gao} [Nonlinear Funct. Anal. Appl. 21, No. 4, 717--725 (2016; Zbl 1431.46008)], the coefficient of weak orthogonality \(w(X)\) defined by \textit{B. Sims} [Bull. Aust. Math. Soc. 49, No. 3, 523--528 (1994; Zbl 0807.47047)], and the coefficient \(R(1,X)\) defined by \textit{T. Domínguez Benavides} [Houston J. Math. 22, No. 4, 835--849 (1996; Zbl 0873.46012)]. Reviewer's remark: When reading the proofs of the theorems, the reader may find it useful to keep in mind that, for superreflexive Banach spaces, the values of the three coefficients mentioned above remain unchanged if \(X\) is replaced by an ultrapower of \(X\).
reviewed by: B. Turett
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B08
zbMATH DE Number: 6905250
zbMATH Keywords: uniform normal structure
zbMATH Keywords: normal structure
zbMATH Keywords: Banaś-Hajnosz-Wedrychowicz type of modulus of convexity
zbMATH Keywords: coefficient of weak orthogonality
zbMATH Keywords: Domínguez-Benavides coefficient
author: Zhanfei Zuo
MaRDI profile type: Publication
full work available at URL: s11784-018-0537-2
OpenAlex ID: W2793646573
cites work: Q3210356
cites work: Q3129867
cites work: A class of spaces with weak normal structure
cites work: Q3998720
cites work: The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces
cites work: Uniform smoothness implies super-normal structure property
cites work: A Fixed Point Theorem for Mappings which do not Increase Distances
cites work: On the modulus of \(u\)-convexity of Ji Gao
cites work: Some estimates for the normal structure coefficient in Banach spaces
cites work: On the modulus of \(U\)-convexity
cites work: Q5267784
cites work: Q3752078
cites work: Some modulus and normal structure in Banach space
cites work: On James and Jordan-von Neumann type constants and normal structure in Banach spaces
DOI: 10.1007/S11784-018-0537-2
description: scientific article; zbMATH DE number 6905250