Logarithmic convexity of extended mean values (Q2781350)
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scientific article; zbMATH DE number 1721094
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Logarithmic convexity of extended mean values |
scientific article; zbMATH DE number 1721094 |
Statements
Logarithmic convexity of extended mean values (English)
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19 March 2002
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logarithmic convexity
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extended mean values
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inequality
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exponential function
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absolutely monotonic function
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arithmetic mean
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logarithmic mean
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identric mean
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The author investigates the logarithmic convexity of the extended mean value introduced by \textit{K. B. Stolarsky} [Math. Mag. 48, 87-92 (1975; Zbl 0302.26003)]. For the arithmetic, logarithmic and identric means of two variables, the inequality \(A+ L< 2I\) is proved. Two open problems are proposed.
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