Functions of class Lip(\(\alpha\) ,p) and their Taylor mean (Q1082557)
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scientific article; zbMATH DE number 3973513
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Functions of class Lip(\(\alpha\) ,p) and their Taylor mean |
scientific article; zbMATH DE number 3973513 |
Statements
Functions of class Lip(\(\alpha\) ,p) and their Taylor mean (English)
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1985
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The object of this paper is to study the rapidity of convergence of the Taylor mean of the Fourier series of \(f(x)\) when \(f(x)\) belongs to the class Lip\((\alpha,p)\). We show that it is of Jackson order provided that a suitable integrability condition is imposed upon the function \(\phi_ x(t)=\{(f(x+t)-2f(x)+f(x-t)\}.\)
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Taylor mean of the Fourier series
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Jackson order
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0.92474836
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0.91205287
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0.8840337
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