Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 838529, 10 pages
doi:10.1155/2009/838529
Research Article

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

Yuming Chu and Yupei Lv

Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received 2 April 2009; Accepted 20 May 2009

Academic Editor: A. Laforgia

Copyright © 2009 Yuming Chu and Yupei Lv. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.