Journal of Applied Mathematics
Volume 2012 (2012), Article ID 182905, 8 pages
http://dx.doi.org/10.1155/2012/182905
Research Article

Optimal Inequalities for Power Means

Yong-Min Li,1 Bo-Yong Long,2 Yu-Ming Chu,1 and Wei-Ming Gong3

1Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
2School of Mathematics Science, Anhui University, Hefei 230039, China
3Department of Mathematics, Hunan City University, Yiyang 413000, China

Received 9 December 2011; Revised 30 January 2012; Accepted 2 February 2012

Academic Editor: Hector Pomares

Copyright © 2012 Yong-Min Li et al. 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 present the best possible power mean bounds for the product for any , , and all with . Here, is the th power mean of two positive numbers and .