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Constructions of Uniformly Convex Functions

  Published:2011-06-14
 Printed: Dec 2012
  • Jonathan M. Borwein,
    Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia
  • Jon Vanderwerff,
    Department of Mathematics, La Sierra University, Riverside, CA, USA
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Abstract

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: convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, norm convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, norm
MSC Classifications: 52A41, 46G05, 46N10, 49J50, 90C25 show english descriptions Convex functions and convex programs [See also 26B25, 90C25]
Derivatives [See also 46T20, 58C20, 58C25]
Applications in optimization, convex analysis, mathematical programming, economics
Frechet and Gateaux differentiability [See also 46G05, 58C20]
Convex programming
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
 

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