New representation of the remainder in the Bernstein approximation
type: Item
instance of: scholarly article
title: New representation of the remainder in the Bernstein approximation
zbMATH Open document ID: 1220.41002
author: Mircea Ivan
author: Ulrich Abel
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-06-20T00:00:00Z
review text: This short note presents a new representation of the remainder in the Bernstein approximation based on divided differences and some immediate applications. It is the only known representation of the remainder in the Bernstein approximation of arbitrary functions as a convex combination of divided differences of second-order on known knots. As an application they obtain sharp inequalities for functions possessing bounded divided differences of second-order and a new proof of the classical Weierstrass approximation theorem.
reviewed by: Francisco Pérez Acosta
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 5909874
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: divided differences
zbMATH Keywords: Weierstrass approximation theorem
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.02.005
OpenAlex ID: W2028319874
Wikidata QID: Q115600863
cites work: On the convergence of derivatives of Bernstein approximation
cites work: Q5819609
cites work: The Remainder of Certain Linear Approximation Formulas in Two Variables
DOI: 10.1016/J.JMAA.2011.02.005
description: scientific article; zbMATH DE number 5909874