Abstract and Applied Analysis
Volume 2013 (2013), Article ID 348326, 12 pages
http://dx.doi.org/10.1155/2013/348326
Research Article

Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means

Tie-Hong Zhao,1 Yu-Ming Chu,2 Yun-Liang Jiang,3 and Yong-Min Li4

1Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China
2School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China
3School of Information & Engineering, Huzhou Teachers College, Huzhou 313000, China
4School of Automation, Southeast University, Nanjing 210096, China

Received 19 January 2013; Accepted 1 February 2013

Academic Editor: Khalil Ezzinbi

Copyright © 2013 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 prove that the double inequalities hold for all with if and only if , , , and , where , , , and are the identric, Neuman-Sándor, quadratic, and contraharmonic means of and , respectively.