Copyright © 2010 Wei-Mao Qian and Ning-Guo Zheng. 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.
For , the generalized logarithmic mean , arithmetic mean and geometric mean of two positive numbers and are defined by , ; , , , ; , , ; , , ; and , respectively. In this paper, we give an answer to the open problem: for , what are the greatest value and the least value , such that the double inequality holds for all ?