Constructions of Uniformly Convex Functions

Canadian mathematical bulletin

Jonathan M. Borwein¹  Jon Vanderwerff² 

[1] Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia;Department of Mathematics, La Sierra University, Riverside, CA, USA

关键词: convex function;    uniformly convex function;    uniformly smooth function;    power type;    Fenchel conjugate;    composition;    norm;   

DOI  :  10.4153/CMB-2011-049-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We give precise conditions under which the composition of a norm with a convex function yields auniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided.

【 授权许可】

Unknown