UNIFORMLY CONVEX FUNCTIONS ON BANACH SPACES

被引：0

作者：

Borwein, J. ^{[1
,2
]}

Guirao, A. J. ^{[3
]}

Hajek, P. ^{[4
]}

Vanderwerff, J. ^{[5
]}

机构：

[1] Dalhousie Univ, Fac Comp Sci, Halifax, NS B3H 1W5, Canada

[2] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW 2308, Australia

[3] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

[4] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic

[5] La Sierra Univ, Dept Math, Riverside, CA 92515 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Convex function; uniformly smooth; uniformly convex; supperreflexive; CONVERGENCE; SMOOTHNESS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a Banach space (X,parallel to . parallel to), we study the connection between uniformly convex funcitons f : X -> R bounded above by parallel to . parallel to(p) and the exictence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X -> R bounded above by parallel to . parallel to(p) if and only if X admits an equivalent norm with modulus of convexity of power type 2

引用

页码：1081 / 1091

页数：11

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