The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications

The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications

We prove that the Hamy symmetric function Fn(x,r)=∑1≤i1<i2<⋯<ir≤n(∏j=1rxij)1/r is Schur harmonic convex for x∈R+n. As its applications, some analytic inequalities including the well-known Weierstrass i...

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Main Authors: Yuming Chu, Yupei Lv
Format: Article
Language:English
Published: SpringerOpen 2009-01-01
Series:Journal of Inequalities and Applications
Online Access:http://dx.doi.org/10.1155/2009/838529
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spelling doaj-e6df16257f3045e7ba26d33f295159a62020-11-24T21:59:43ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-01200910.1155/2009/838529The Schur Harmonic Convexity of the Hamy Symmetric Function and Its ApplicationsYuming ChuYupei LvWe prove that the Hamy symmetric function Fn(x,r)=∑1≤i1<i2<⋯<ir≤n(∏j=1rxij)1/r is Schur harmonic convex for x∈R+n. As its applications, some analytic inequalities including the well-known Weierstrass inequalities are obtained. http://dx.doi.org/10.1155/2009/838529
collection DOAJ
language English
format Article
sources DOAJ
author Yuming Chu
Yupei Lv
spellingShingle Yuming Chu
Yupei Lv
The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications
Journal of Inequalities and Applications
author_facet Yuming Chu
Yupei Lv
author_sort Yuming Chu
title The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications
title_short The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications
title_full The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications
title_fullStr The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications
title_full_unstemmed The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications
title_sort schur harmonic convexity of the hamy symmetric function and its applications
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2009-01-01
description We prove that the Hamy symmetric function Fn(x,r)=∑1≤i1<i2<⋯<ir≤n(∏j=1rxij)1/r is Schur harmonic convex for x∈R+n. As its applications, some analytic inequalities including the well-known Weierstrass inequalities are obtained.
url http://dx.doi.org/10.1155/2009/838529
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AT yupeilv schurharmonicconvexityofthehamysymmetricfunctionanditsapplications
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