Approximation by \(q\)-Durrmeyer operators
type: Item
instance of: scholarly article
title: Approximation by \(q\)-Durrmeyer operators
zbMATH Open document ID: 1198.41008
author: Zoltán Finta
author: Vijay Gupta
published in: Journal of Applied Mathematics and Computing
publication date: 2009-10-26T00:00:00Z
review text: The \(q\)-Durrmeyer operators were recently introduced by \textit{V. Gupta} [Appl. Math. Comput. 197, No.~1, 172--178 (2008; Zbl 1142.41008)]. In the present paper, the authors establish new and interesting approximation properties of the mentioned operators. The first main result,contained in Theorem 1, expresses the degree of local approximation of a function \(f\), continuous on the compact interval \([0,1]\) using the \(q\)-Durrmeyer operators in terms of first and respectively second order moduli of smoothness. the second main result, contained in Theorem 3, expresses the degree of global approximation in terms of second order modulus of smoothness and respectively Ditzian-Totik moduli of first order. Finally, a simultaneous approximation theorem for the case when the approximated function is a polynomial is established.
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 5620589
zbMATH Keywords: \(q\)-Durrmeyer operators
zbMATH Keywords: modulu of smoothness
zbMATH Keywords: \(K\)-functionals
zbMATH Keywords: simultaneous approximation
reviewed by: Dan Bărbosu
MaRDI profile type: Publication
full work available at URL: s12190-008-0141-5
OpenAlex ID: W2000349002
cites work: Q4273944
cites work: Q3817079
cites work: Some approximation properties of \(q\)-Durrmeyer operators
cites work: Polynomial interpolation at points of a geometric mesh on a triangle
cites work: Q4365448
cites work: Voronovskaya-type formulas and saturation of convergence for \(q\)-Bernstein polynomials for \(0 < q < 1\)
DOI: 10.1007/S12190-008-0141-5
Recommended article: Some approximation properties of \(q\)-Durrmeyer operators
Recommended article: Approximation by \(q\)-Baskakov Durrmeyer type operators
Recommended article: A note on approximation properties of \(q\)-Durrmeyer operators
Recommended article: Some approximation properties of \(q\)-Durrmeyer-Schurer operators
Recommended article: Approximation properties by \(q\)-Durrmeyer-Stancu operators
Recommended article: Approximation by a complex \(q\)-Durrmeyer type operator
Recommended article: Approximation by Durrmeyer-type operators
Recommended article: Some approximation properties of \(q\)-Baskakov-Durrmeyer operators
Recommended article: Approximation properties of \(q\)-Baskakov-Durrmeyer-Stancu operators
Recommended article: On Approximation by $(p,q)$-Meyer-König-Zeller Durrmeyer Operators
description: scientific article; zbMATH DE number 5620589