Limit properties in a family of quasi-arithmetic means (Q304021)
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scientific article; zbMATH DE number 6618931
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limit properties in a family of quasi-arithmetic means |
scientific article; zbMATH DE number 6618931 |
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Limit properties in a family of quasi-arithmetic means (English)
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23 August 2016
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The author gives certain necessary and sufficient conditions for a one-parameter family of quasi-arithmetic means generated by functions satisfying some smoothness conditions, to have a similar property to the classical power mean, which has the maximum (or minimum) of their arguments, as the limit, when the exponent tends to \(+\infty\) (or \(-\infty\)). The results are strongly connected with some operators introduced by Mikusiński, resp. Páles.
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quasi-arithmetic means
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limit properties
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Arrow-Pratt index
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scale
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