Degree of approximation of functions in \(L^p\) by power series method of summation (Q2725627)
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scientific article; zbMATH DE number 1619479
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Degree of approximation of functions in \(L^p\) by power series method of summation |
scientific article; zbMATH DE number 1619479 |
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12 July 2001
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power series method
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degree of approximation
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Fourier series
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Dini-Lipschitz condition
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Degree of approximation of functions in \(L^p\) by power series method of summation (English)
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This paper is closely related to the paper [\textit{P. Chandra} and \textit{R. N. Mohapatra}, Approximation Theory Appl. 4, No. 2, 49-54 (1988; Zbl 0673.42002)]. The paper contains some improvements of estimates of \(\|D(r,f)-f\|_p\), where \(D(r,f)\) are some means depending on \(r\in (0,1]\) of \(n\)th partial sums of Fourier series of \(f\). Here \(f\) belongs to \(\text{Lip}(\alpha, p)\), \(p\geq 1\), \(0<\alpha\leq 1\), or \(f\) satisfies the generalized Dini-Lipschitz condition.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00019].
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