On the asymptotic behaviour of \(\varphi\)-means (Q1900354)
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scientific article; zbMATH DE number 811170
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the asymptotic behaviour of \(\varphi\)-means |
scientific article; zbMATH DE number 811170 |
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On the asymptotic behaviour of \(\varphi\)-means (English)
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17 March 1996
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The author offers a generalization of a result by \textit{R. P. Boas} and \textit{J. L. Brenner} [J. Math. Anal. Appl. 123, 262-264 (1987; Zbl 0614.26001)], which states that, under certain conditions, the limit of \(f^{-1}(\sum p_k f(x_k + t)) - t\) as \(t\) goes to \(+ \infty\) is \(\sum p_k x_k\) \((\sum p_k = 1)\), to (Stieltjes) integral means on masses with compact support.
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integral mean values
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monotonic differentiable functions
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Stieltjes integral means
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masses with compact support
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