Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic MeansReport as inadecuate




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Abstract and Applied AnalysisVolume 2013 2013, Article ID 348326, 12 pages

Research Article

Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China

School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China

School of Information and Engineering, Huzhou Teachers College, Huzhou 313000, China

School 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.





Author: Tie-Hong Zhao, Yu-Ming Chu, Yun-Liang Jiang, and Yong-Min Li

Source: https://www.hindawi.com/



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