Sharp bounds involving the Sandor-Yang means in terms of other bivariate means

Shao Yun Li, Fang Jin, Hui Zuo Xu

Abstract


In this paper, we present the best possible parameters ${\alpha _1},{\alpha _2},{\alpha _3},{\alpha _4},{\beta _1},{\beta _2},{\beta _3},{\beta _4} \in [0,1]$ such that the double inequalities hold for all $a,b > 0$ with $a \neq b$. Here $G\left( {a,b} \right)$, $A\left( {a,b} \right)$ and $Q\left( {a,b} \right)$ denote respectively the classical geometric, arithmetic and quadratic means of $a$ and $b$, and ${R_{GA}}\left( {a,b} \right) = X\left( {a,b} \right)$, ${R_{AG}}\left( {a,b} \right) = I\left( {a,b}\right)$, ${R_{QA}}\left( {a,b} \right)$ and ${R_{AQ}}\left( {a,b} \right)$ are S\'{a}ndor, identric and two S\'{a}ndor -Yang means derived from the Schwab-Borchardt mean.

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Published: 2019-05-09

How to Cite this Article:

Shao Yun Li, Fang Jin, Hui Zuo Xu, Sharp bounds involving the Sandor-Yang means in terms of other bivariate means, Adv. Inequal. Appl., 2019 (2019), Article ID 9

Copyright © 2019 Shao Yun Li, Fang Jin, Hui Zuo Xu. 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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