Constructions of Uniformly Convex Functions

Borwein, Jonathan M. ; Vanderwerff, Jon

Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 697-707

Résumé

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.

Détail

DOI : 10.4153/CMB-2011-049-2

Mots-clés : 52A41, 46G05, 46N10, 49J50, 90C25, convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, norm

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