Table of Contents
Chinese Journal of Mathematics
Volume 2013, Article ID 852516, 7 pages
http://dx.doi.org/10.1155/2013/852516
Research Article

Optimal Lehmer Mean Bounds for the Combinations of Identric and Logarithmic Means

1College of Nursing, Huzhou Teachers College, Huzhou 313000, China
2School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, China

Received 11 July 2013; Accepted 5 August 2013

Academic Editors: M. Coppens, Y. Miao, and P.-y. Nie

Copyright © 2013 Xu-Hui Shen 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

For any , we answer the questions: what are the greatest values and and the least values and , such that the inequalities and hold for all with ? Here, , , and denote the identric, logarithmic, and th Lehmer means of two positive numbers and , respectively.