Pointwise analog of the Jackson approximation theorem
type: Item
instance of: scholarly article
title: Pointwise analog of the Jackson approximation theorem
zbMATH Open document ID: 1236.41027
published in: Applied Mathematics and Computation
publication date: 2011-12-29T00:00:00Z
review text: Let \(X=X_Q\) be the set of real--valued, \(2 \pi\)--periodic, continuous functions on \(Q\), let \(E_n(f)_{X_{[x-\pi,x+\pi]}}\) denote the best approximation of \(f(t)\) by trigonometric polynomials of degree at most \(n\), and let \(\omega f( \delta)_X\) denote the modulus of continuity. A typical result is that if \(f \in X\), then there is a \(\delta > 0\) such that \(E_n(f)_{X_{[x-\delta,x+\delta]}} \leq K \omega f( {{\pi}\over {n+1}})_{X_{[x-\pi,x+\pi]}}\). Similar results are presented for Lebesgue integrable functions.
reviewed by: Richard A. Zalik
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 5992856
zbMATH Keywords: approximation
zbMATH Keywords: best approximation
zbMATH Keywords: Jackson's theorem
zbMATH Keywords: trigonometric polynomials
author: W. Łenski
MaRDI profile type: Publication
full work available at URL: j.amc.2011.06.036
OpenAlex ID: W2084812361
cites work: On the degree of convergence of Fejér-Lebesgue sums
cites work: Q5621638
cites work: Q3969334
DOI: 10.1016/J.AMC.2011.06.036
description: scientific article; zbMATH DE number 5992856