Sharp bounds for Sandor-Yang means in terms of Lehmer means

Jun Li Wang, Hui Zuo Xu, Wei Mao Qian

Abstract


In the article, the authors prove that the double inequalities $L_{0} (a,b)<S_{AQ} (a,b)<L_{1/6} (a,b)$,$L_{0} (a,b)<S_{QA} (a,b)<L_{1/3} (a,b)$ holds for all $a,b>0$ with $a\ne b$, where $L_{p} (a,b)=\left( {a^{p+1}+b^{p+1}}\right)/\left( {a^{p}+b^{p}} \right)$ is the $p$th Lehmer mean, and $S_{AQ} (a,b)$, $S_{QA} (a,b)$ are the S\'{a}ndor-Yang means, respectively.

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Published: 2017-12-05

How to Cite this Article:

Jun Li Wang, Hui Zuo Xu, Wei Mao Qian, Sharp bounds for Sandor-Yang means in terms of Lehmer means, Advances in Inequalities and Applications, Vol 2018 (2018), Article ID 2

Copyright © 2018 Jun Li Wang, Hui Zuo Xu, Wei Mao Qian. 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.

Advances in Inequalities and Applications

ISSN 2050-7461

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