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Constructions of Uniformly Convex Functions

Published online by Cambridge University Press:  20 November 2018

Jonathan M. Borwein  and
Jon Vanderwerff
Jonathan M. Borwein
Affiliation:
Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australiae-mail: jonathan.borwein@newcastle.edu.au
Jon Vanderwerff
Affiliation:
Department of Mathematics, La Sierra University, Riverside, CA, USAe-mail: jvanderw@lasierra.edu
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Abstract

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We give precise conditions under which the composition of a norm with a convex function yields a uniformly 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.

Keywords

52A4146G0546N1049J5090C25convex functionuniformly convex functionuniformly smooth functionpower typeFenchel conjugatecompositionnorm
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 697 - 707
Copyright
Copyright © Canadian Mathematical Society 2012

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