Abstract and Applied Analysis
Volume 2012 (2012), Article ID 302635, 9 pages
http://dx.doi.org/10.1155/2012/302635
Research Article

Optimal Bounds for Neuman-Sándor Mean in Terms of the Convex Combinations of Harmonic, Geometric, Quadratic, and Contraharmonic Means

Tie-Hong Zhao,1 Yu-Ming Chu,2 and Bao-Yu Liu3

1Department of Mathematics, Hangzhou Normal University, Hangzhou 313036, China
2School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China
3School of Science, Hangzhou Dianzi University, Hangzhou 310018, China

Received 15 October 2012; Accepted 5 December 2012

Academic Editor: Julian López-Gómez

Copyright © 2012 Tie-Hong Zhao 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 lower and upper bounds for the Neuman-Sándor mean in terms of the convex combinations of either the harmonic and quadratic means or the geometric and quadratic means or the harmonic and contraharmonic means.