Approximation properties of recursively defined Bernstein-type operators
type: Item
instance of: scholarly article
title: Approximation properties of recursively defined Bernstein-type operators
zbMATH Open document ID: 0865.41027
author: Michele Campiti
author: Giorgio Metafune
published in: Journal of Approximation Theory
publication date: 1997-02-20T00:00:00Z
review text: The authors consider polynomial type operators having the form \(A_n(f;x)= \sum^{k=n}_{k=0} \alpha_{n,k} x^k(1-x)^{n-k} f({k\over n})\) with \(n\in\mathbb{N} =\{1,2,\dots\}\), \(f\in C([0,1], \mathbb{R})\), \(x\in [0,1]\), \(\alpha_{n+1,k} =\alpha_{n,k} +\alpha_{n,k-1}\) for \(k\in \overline {1,n}\) and \(\alpha_{n,0} =\lambda_n\), \(\alpha_{n,n} =\rho_n\), where \((\lambda_n)_{n\in \mathbb{N}} \), \((\rho_n)_{n\in\mathbb{N}}\) are fixed sequences of real numbers. The authors study the uniform convergence of these operators together with some quantitative and regularity properties. Finally, in some particular cases, they investigate the behavior of the iterates.
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 980673
zbMATH Keywords: generalization of Bernstein operators
zbMATH Keywords: uniform convergence
zbMATH Keywords: quantitative estimates
zbMATH Keywords: behavior of the iterates
reviewed by: Ion Badea
MaRDI profile type: Publication
full work available at URL: jath.1996.0104
OpenAlex ID: W2040739461
DOI: 10.1006/JATH.1996.0104
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description: scientific article; zbMATH DE number 980673