A sharp double inequality between harmonic and identric means (Q642726)
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scientific article; zbMATH DE number 5964408
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sharp double inequality between harmonic and identric means |
scientific article; zbMATH DE number 5964408 |
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A sharp double inequality between harmonic and identric means (English)
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27 October 2011
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Summary: We find the greatest value \(p\) and the least value \(q\) in \((0, 1/2)\) such that the double inequality \(H(pa + (1 - p)b, pb + (1 - p)a) < I(a, b) < H(qa + (1 - q)b, qb + (1 - q)a)\) holds for all \(a, b > 0\) with \(a \neq b\). Here, \(H(a, b)\), and \(I(a, b)\) denote the harmonic and identric means of two positive numbers \(a\) and \(b\), respectively.
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harmonic mean
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identric mean
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0.9102262
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0.9094031
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0.90193284
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0.8995129
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0.8995129
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0.89185673
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0.89185673
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0.8915175
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0.8913963
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