Complete asymptotic expansion for generalized Favard operators
type: Item
instance of: scholarly article
title: Complete asymptotic expansion for generalized Favard operators
zbMATH Open document ID: 1262.41023
author: Ulrich Abel
author: Paul L. Butzer
published in: Constructive Approximation
publication date: 2012-02-14T00:00:00Z
review text: The authors consider, for a sequence of positive reals \(\sigma_n\), a generalisation \(F_n\), \(\sigma_n\) of the Favard operators [\textit{W. Grawronski} and \textit{U. Stadtmüller}, J. Approximation Theory 34, 384--396 (1982; Zbl 0484.41019)], and obtain a complete asymptotic expansion for the sequence \((F_n,\sigma_n f)(x)\) \((n\to\infty)\) for \(f\) sufficiently smooth. They also study the simultaneous approximation and a truncated version of these operators.
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 6006497
zbMATH Keywords: Approximation by positive operators
zbMATH Keywords: rate of convergence
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: simultaneous approximation
MaRDI profile type: Publication
full work available at URL: s00365-011-9134-y
OpenAlex ID: W2014208921
Wikidata QID: Q115600862
cites work: Q4746228
cites work: Saturation for Farvard operators in weighted function spaces
cites work: Q5621638
cites work: Sur le multiplicateurs d'interpolation
cites work: Approximation of continuous functions by generalized Favard operators
cites work: Asymptotic formulas for multivariate Bernstein-Schoenberg operators
cites work: Asymptotic expansion of multivariate conservative linear operators
cites work: Q4788704
cites work: On the generalized Favard-Kantorovich and Favard-Durrmeyer operators in exponential function spaces
cites work: On the generalized Favard operators
cites work: Approximation properties of the generalized Favard-Kantorovich operators
cites work: Q5604622
cites work: Asymptotic expansions for multivariate polynomial approximation
DOI: 10.1007/S00365-011-9134-Y
description: scientific article; zbMATH DE number 6006497