Rate of convergence of Baskakov-Bézier type operators for locally bounded functions.
type: Item
instance of: scholarly article
title: Rate of convergence of Baskakov-Bézier type operators for locally bounded functions.
zbMATH Open document ID: 1061.41011
DOI: 10.1016/S0898-1221(02)00269-9
author: Xiao-Ming Zeng
author: Vijay Gupta
publication date: 2003-12-14T00:00:00Z
review text: Let \(b_{n,k}(x)= {n+k-1\choose k} x^k (1+x)^{-n-k}\) and \(J_{n,k}(x)=\sum\limits_{j=k}^{\infty} b_{n,j}(x), \alpha\geq 1\). The Baskakov-Bézier operator \(B_{n,\alpha}\) is defined by \[ B_{n,\alpha}(f,x)=\sum\limits_{k=0}^{\infty}f(\frac{k}{n})[J_{n,k}^\alpha(x)-J_{n,k+1}^\alpha(x)]. \] In this paper the authors studied the rate of convergence of the operator \(B_{n,\alpha}\) for locally bounded functions by using some results of probability theory. The estimate is essentially the best possible. The method is not new (cf. \textit{S. Guo} and \textit{M. K. Khan} [J. Approximation Theory 58, No.1, 90--101 (1989; Zbl 0683.41030)]).
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 2017159
zbMATH Keywords: Rate of convergence
zbMATH Keywords: Operator of probabilistic type
zbMATH Keywords: Lebesgue-Stieltjes
zbMATH Keywords: integral
MaRDI profile type: Publication
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full work available at URL: s0898-1221(02)00269-9
OpenAlex ID: W1991533588
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2017159