The Bézier variant of Kantorovitch operators
type: Item
instance of: scholarly article
title: The Bézier variant of Kantorovitch operators
zbMATH Open document ID: 1053.65098
DOI: 10.1016/S0898-1221(04)90019-3
publication date: 2004-06-15T00:00:00Z
review text: The author introduces the following generalized Kantorovich-type operator \[ B_n(f, x)=n\sum_{k=1}^\infty p_{n,k}(x)\int_{I_k}f(t)dt, \] where \[ I_k=[k/n, (k+1)/n] \] and \[ p_{n,k}(x)=(-1)^k\frac{x^k}{k!}\phi_n^{(k)}(x). \] Here \(\phi_n(x)\) is a scalar function, which for special values reduces the operator \(B_n(f, x)\) to the well-known Szasz-Kantorovich operators and Baskakov-Kantorovich operators. Estimates for the rate of convergence of the Bezier variant of these generalized operators are derived for bounded variation functions.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 2075454
zbMATH Keywords: integral operators
zbMATH Keywords: convergence
zbMATH Keywords: bounded variation
zbMATH Keywords: total variation
zbMATH Keywords: Baskakov-Kantorovich operators
zbMATH Keywords: Szasz-Kantorovich operators
author: Vijay Gupta
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
cites work: \(L_ p\)-approximation by Szász-Mirakjan-Kantorovitch operators
cites work: Q3041680
cites work: Asymptotic properties of positive summation-integral operators
cites work: Q3817079
cites work: Uniform approximation by Szasz-Mirakjan type operators
cites work: Problems and solutions concerning Kantorovich operators
cites work: On the rate of convergence of the generalized Szász type operators for functions of bounded variation
cites work: Rate of convergence of Baskakov-Bézier type operators for locally bounded functions.
cites work: Convexité, complète monotonie et inégalités sur les fonctions zèta et gamma, sur les fonctions des opérateurs de Baskakov et sur des fonctions arithmétiques
cites work: AN ESTIMATE OF THE RATE OF CONVERGENCE OF A BÉZIER VARIANT OF THE BASKAKOV-KANTOROVICH OPERATORS FOR BOUNDED VARIATION FUNCTIONS
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2075454