Generalized Bernstein-Durrmeyer operators and the associated limit semigroup
type: Item
instance of: scholarly article
title: Generalized Bernstein-Durrmeyer operators and the associated limit semigroup
zbMATH Open document ID: 0935.41020
author: Antonio Attalienti
published in: Journal of Approximation Theory
publication date: 2000-05-02T00:00:00Z
review text: In recent years there have been quite a few generalizations of the Bernstein-Durrmeyer operators either by shifting the exponents in the Bernstein polynomials in various ways, or by shifting the abscissae where the function is evaluated in various ways. The current paper is an attempt to put many of the generalizations under one roof. The author applies the Lototsky--Schnabl operators to a generalization of the Beta operators, originally introduced by Lupaş. Investigating separately properties of the two operators the author proves some of the classical error estimates involving the first and (sometimes) the second moduli of smoothness of the function. Also he is able to obtain a Voronovskaja-type result for the generalized operators. The last part of the paper is devoted to the investigation of the relations between the new operators and the associated semigroup and its infinitesimal generator.
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 1346404
zbMATH Keywords: Bernstein-Durrmeyer operators
zbMATH Keywords: Voronovskaja-type results
zbMATH Keywords: infinitesimal generator
reviewed by: D. Leviatan
MaRDI profile type: Publication
full work available at URL: jath.1999.3329
OpenAlex ID: W2023572583
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DOI: 10.1006/JATH.1999.3329
description: scientific article; zbMATH DE number 1346404