Geodesic
Constructions of Uniformly Convex Functions
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 697-707

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DOI

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.
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 
Borwein, Jonathan M.; Vanderwerff, Jon. Constructions of Uniformly Convex Functions. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 697-707. doi: 10.4153/CMB-2011-049-2
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     author = {Borwein, Jonathan M. and Vanderwerff, Jon},
     title = {Constructions of {Uniformly} {Convex} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {697--707},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-049-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-049-2/}
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