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The Schur harmonic convexity for a class of symmetric functions

โœ Scribed by Chu Yuming; Sun Tianchuan

Book ID
108422436
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
191 KB
Volume
30
Category
Article
ISSN
0252-9602

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## Abstract This paper investigates the Schur multiplicative and harmonic convexities of the complete symmetric function \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$F\_n(x,r)=\sum \_{i\_1+i\_2+\cdots +i\_n=r}x\_1^{i\_1}x\_2^{i\_2}\ldots x\_n^{i\_n}$\end{document} an

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The Schur-convexity at the upper and lower limits of the integral for the mean of a convex function is researched. As applications, a form with a parameter of Stolarsky's mean is obtained and a relevant double inequality that is an extension of a known inequality is established.