Bounds for Bernstein basis functions and Meyer-König and Zeller basis functions
type: Item
instance of: scholarly article
title: Bounds for Bernstein basis functions and Meyer-König and Zeller basis functions
zbMATH Open document ID: 0909.41015
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-10-26T00:00:00Z
review text: The main of this paper is the following result: Let \(n,k,p\in \{0,1,2, \dots\}\) and \(C_p= (p+ 0,5)^{p+0,5} (p!)^{-1} e^{-p-0,5}\). For all \(k,x\) such that \(p\leq k\leq n-p\), \(x\in(0,1)\) \({n\choose k} x^k(1-x)^{n-k} <C_p (nx(1-x))^{-0,5}\). If \(0\leq k\leq n\) and \(x\in(0,1]\) then \({n+k-1 \choose k} x^k(1-x)^n <(2enx)^{-0,5}\). The coefficients \(C_p\), \((2e)^{-0,5} \approx 0.4288819\) and the estimate order \(n^{-0,5}\) are the best possible.
Mathematics Subject Classification ID: 41A44
zbMATH DE Number: 1215741
author: Xiao-Ming Zeng
reviewed by: Ion Badea
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5819
OpenAlex ID: W1532062633
cites work: Q3840971
cites work: Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation
cites work: On the rate of convergence of the Durrmeyer operator for functions of bounded variation
cites work: On the rate of convergence of the integrated Meyer-König and Zeller operators for functions of bounded variation
cites work: Q4857639
cites work: Q4864329
DOI: 10.1006/JMAA.1997.5819
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description: scientific article; zbMATH DE number 1215741