Journal of Applied Mathematics
Volume 2012 (2012), Article ID 480689, 8 pages
http://dx.doi.org/10.1155/2012/480689
Research Article

Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means

Wei-Mao Qian1 and Bo-Yong Long2

1School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China
2School of Mathematics Science, Anhui University, Hefei 230039, China

Received 29 January 2012; Revised 19 February 2012; Accepted 12 March 2012

Academic Editor: Yuri Sotskov

Copyright © 2012 Wei-Mao Qian and Bo-Yong Long. 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 sharp upper and lower generalized logarithmic mean bounds for the geometric weighted mean of the geometric and harmonic means.