Canad. Math. Bull. 55(2012), 697-707
Printed: Dec 2012
Jonathan M. Borwein,
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.
convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, norm
52A41 - Convex functions and convex programs [See also 26B25, 90C25]
46G05 - Derivatives [See also 46T20, 58C20, 58C25]
46N10 - Applications in optimization, convex analysis, mathematical programming, economics
49J50 - Frechet and Gateaux differentiability [See also 46G05, 58C20]
90C25 - Convex programming