Best possible inequalities between generalized logarithmic mean and classical means (Q963180)
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scientific article; zbMATH DE number 5690923
| Language | Label | Description | Also known as |
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| English | Best possible inequalities between generalized logarithmic mean and classical means |
scientific article; zbMATH DE number 5690923 |
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Best possible inequalities between generalized logarithmic mean and classical means (English)
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8 April 2010
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Summary: We answer the question: for \(\alpha ,\beta ,\gamma \in (0,1)\) with \(\alpha +\beta +\gamma =1\), what are the greatest value \(p\) and the least value \(q\), such that the double inequality \(L_p(a,b)0\) with \(a\neq b\)? Here \(L_p(a,b), A(a,b), G(a,b)\), and \(H(a,b)\) denote the generalized logarithmic, arithmetic, geometric, and harmonic means of two positive numbers \(a\) and \(b\), respectively.
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