On approximation of \(2\pi \)-periodic functions in Hölder spaces
type: Item
instance of: scholarly article
title: On approximation of \(2\pi \)-periodic functions in Hölder spaces
zbMATH Open document ID: 1065.41028
published in: Hokkaido Mathematical Journal
publication date: 2005-03-07T00:00:00Z
review text: The paper is devoted to study the approximation of \(2\pi\) periodic functions belonging to generalized Hölder spaces.In the first part,some results concerning the moduli of smoothness of first and higher order are recalled. Then, a family of integral operators is introduced. Two very interesting and nice results in connection with these operators are established. The first of them contains the approximation order in terms of higher order moduli of smoothness. The second expresses the asymptotic behaviour of approximation when the approximated function belong to a generalized Hölder space. The results are applied to Vallée-Poussin operators and to Abel means.
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 2140987
zbMATH Keywords: Hölder space
zbMATH Keywords: approximation theorem
zbMATH Keywords: Valle-Poussin integral operator
zbMATH Keywords: Abel mean
author: L. Rempulska
author: Zbigniew Walczak
reviewed by: Dan Bărbosu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1285851915
OpenAlex ID: W1980471677
DOI: 10.14492/HOKMJ/1285851915
description: scientific article; zbMATH DE number 2140987