Direct estimate for Bernstein polynomials
type: Item
instance of: scholarly article
title: Direct estimate for Bernstein polynomials
zbMATH Open document ID: 0814.41005
author: Z. Ditzian
published in: Journal of Approximation Theory
publication date: 1994-09-27T00:00:00Z
review text: The following pointwise approximation for the Bernstein polynomials \(B_ n (f,x)= \sum_{k=0}^ n {\binom nk} x^ k (1-x)^{n -k} f(k/n)\) are proved: \[ | B_ n (f,x)- f(x)|\leq C\omega^ 2_{\varphi^ \lambda} (f, n^{-1/2} \varphi (x)^{1- \lambda}), \qquad 0\leq \lambda\leq 1, \quad \varphi(x)^ 2= x(1-x). \] This estimates yields a unified treatment of the classical estimate \((\lambda=0)\) and the norm estimate \((\lambda=1)\).
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 645064
zbMATH Keywords: Bernstein polynomials
reviewed by: Fritz Haslinger
MaRDI profile type: Publication
full work available at URL: jath.1994.1120
OpenAlex ID: W1978526666
DOI: 10.1006/JATH.1994.1120
description: scientific article; zbMATH DE number 645064