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

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.