Improved upper and lower bounds for the difference \(A_n-G_n\) (Q5948866)
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scientific article; zbMATH DE number 1672108
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Improved upper and lower bounds for the difference \(A_n-G_n\) |
scientific article; zbMATH DE number 1672108 |
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Improved upper and lower bounds for the difference \(A_n-G_n\) (English)
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12 November 2001
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The author obtains new refinements of certain inequalities of Cartwright and Field, as well as Alzer, on the difference \(A-G\), where \(A\) and \(G\) denote the arithmetic, resp. geometric means of \(n\) positive numbers. The proofs are based on interesting applications of the Cauchy mean value theorem of differential calculus.
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inequalities for finite sums
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arithmetic mean
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geometric mean
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Cauchy mean value theorem
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