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arXiv · 1405.4384

Sharp Bounds for Neuman Means in Terms of Geometric, Arithemtic and Quadratic Means

Zhi-Jun Guo·Yan Zhang·Yu-Ming Chu·Ying-Qing Song
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Abstract

In this paper, we find the greatest values $\alpha_{1}$, $\alpha_{2}$, $\alpha_{3}$, $\alpha_{4}$, $\alpha_{5}$, $\alpha_{6}$, $\alpha_{7}$, $\alpha_{8}$ and the least values $\beta_{1}$, $\beta_{2}$, $\beta_{3}$, $\beta_{4}$, $\beta_{5}$, $\beta_{6}$, $\beta_{7}$, $\beta_{8}$ such that the double inequalities $$A^{\alpha_{1}}(a,b)G^{1-\alpha_{1}}(a,b) 0$ with $a\neq b$, where $G$, $A$ and $Q$ are respectively the geometric, arithmetic and quadratic means, and $N_{GA}$, $N_{AG}$, $N_{AQ}$ and $N_{QA}$ are the Neuman means derived from the Schwab-Borchardt mean.

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Zhi-Jun Guo, Yan Zhang, Yu-Ming Chu, Ying-Qing Song. 2014-05-17. Sharp Bounds for Neuman Means in Terms of Geometric, Arithemtic and Quadratic Means. https://arxiv.org/abs/1405.4384

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