Sharp bounds for power mean in terms of generalized Heronian mean (Q554928)
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scientific article; zbMATH DE number 5930770
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sharp bounds for power mean in terms of generalized Heronian mean |
scientific article; zbMATH DE number 5930770 |
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Sharp bounds for power mean in terms of generalized Heronian mean (English)
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22 July 2011
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Summary: For \(1 < r < +\infty\), we find the least value \(\alpha\) and the greatest value \(\beta\) such that the inequality \(H_{\alpha}(a, b) < A_r(a, b) < H_{\beta}(a, b)\) holds for all \(a, b > 0\) with \(a \neq b\). Here, \(H_{\omega}(a, b)\) and \(A_r(a, b)\) are the generalized Heronian and the power means of two positive numbers \(a\) and \(b\), respectively.
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power mean
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Heronian mean
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