Journal of Inequalities and Applications

Volume 2010 (2010), Article ID 806825, 10 pages

doi:10.1155/2010/806825

## Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means

^{1}College of Mathematics and Econometrics, Hunan University, Changsha 410082, China^{2}School of Mathematical Sciences, Anhui University, Hefei 230039, China^{3}Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received 20 October 2009; Revised 16 December 2009; Accepted 1 February 2010

Academic Editor: Alexander I. Domoshnitsky

Copyright © 2010 Bo-Yong Long and Yu-Ming Chu. 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

For