Jackson order of approximation by Chebyshev-Fourier series
type: Item
instance of: scholarly article
title: Jackson order of approximation by Chebyshev-Fourier series
zbMATH Open document ID: 0855.42018
DOI: 10.1007/BF00052202
author: Ágota P. Horváth
published in: Acta Mathematica Hungarica
publication date: 1997-01-22T00:00:00Z
review text: \textit{G. Mastroianni} and \textit{J. Szabados} [Suppl. Rend. Circ. Mat. Palermo, II. Ser. 33, 375-386 (1994; Zbl 0837.41003)] raised and solved some problems of finding classes of functions where the order of Lagrange interpolation which follows from the global properties of the function can be improved by amending the local properties of the function. The author of the present paper investigates whether the function classes found in the previous problems are as good in the case of approximation by Chebyshev-Fourier series as in the interpolation case. He deals with the continuous case only, but obtains the same conclusion without assuming the continuity of the piecewise second derivative of the function as it was needed in the interpolation case. His first theorem deals with approximation by Chebyshev series of first kind, and the second one with second kind. Using these results he is able to give some estimations in the case of weighted approximation by ultraspherical Fourier series.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 897180
zbMATH Keywords: approximation by Chebyshev-Fourier series
zbMATH Keywords: weighted approximation by ultraspherical Fourier series
reviewed by: László Leindler
MaRDI profile type: Publication
cites work: Q4324802
cites work: On the Lagrange interpolation for a subset of \(C^ k\) functions
cites work: Jackson order of approximation by Lagrange interpolation. II
cites work: Q3264312
cites work: Q4052481
full work available at URL: https://doi.org/10.1007/bf00052202
OpenAlex ID: W1779739505
description: scientific article; zbMATH DE number 897180