Symmetrization, convexity and applications

Based on permutation enumeration of the symmetric group and ‘generalized’ barycentric coordinates on arbitrary convex polytope, we develop a technique to obtain symmetrization procedures for functions that provide a unified framework to derive new Hermite–Hadamard type inequalities. We also present...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-08, Vol.240, p.149-160
Main Authors: Guessab, Allal, Guessab, Florian
Format: Article
Language:English
Subjects:
Barycentric coordinates
Convex functions
Convex polytopes
Convexity
Enumeration
Group theory
Hermite–Hadamard inequality
Inequalities
Mathematical analysis
Mathematical models
Mathematics
Numerical Analysis
Permutations
Polytopes
Symmetrization of functions
Wright functions
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Summary:Based on permutation enumeration of the symmetric group and ‘generalized’ barycentric coordinates on arbitrary convex polytope, we develop a technique to obtain symmetrization procedures for functions that provide a unified framework to derive new Hermite–Hadamard type inequalities. We also present applications of our results to the Wright-convex functions with special emphasis on their key role in convexity. In one dimension, we obtain (up to a positive multiplicative constant) a method of symmetrization recently introduced by Dragomir (2014) [3], and also by El Farissi et al. (2012/2013) [4]. So our approach can be seen as a multivariate generalization of their method.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.04.063