A family of univariate rational Bernstein operators
type: Item
instance of: scholarly article
title: A family of univariate rational Bernstein operators
zbMATH Open document ID: 1180.41010
author: Paula Piţul
author: P. Sablonnière
published in: Journal of Approximation Theory
publication date: 2009-12-03T00:00:00Z
review text: A new family of positive rational Bernstein operators of the form \[ R_n(f;\,x)=P_n(f;\,x)/Q_{n-1}(f;\,x)\,,\;\;f\in \mathbb C\;([0,\;1])\,, \] is studied. It is proven that it possesses linear precision, shape preserving and total variation diminishing property. Formulas for the first and second derivatives are carried out. Some convergence results, error estimations and Voronovskaja-type theorems are also given.
reviewed by: Ljubiša Kocić
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 5641722
zbMATH Keywords: positive operators
zbMATH Keywords: rational approximants
MaRDI profile type: Publication
full work available at URL: j.jat.2007.11.005
OpenAlex ID: W2069845066
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DOI: 10.1016/J.JAT.2007.11.005
description: scientific article; zbMATH DE number 5641722