The Baskakov operators for functions of two variables
type: Item
instance of: scholarly article
title: The Baskakov operators for functions of two variables
zbMATH Open document ID: 0955.41018
author: M. Gurdek
author: M. Skorupka
author: L. Rempulska
published in: Collectanea Mathematica
publication date: 2001-02-14T00:00:00Z
full work available at URL: https://eudml.org/doc/42704
review text: The sequences \((A_{m,n})_{m,n \in\mathbb{N}_0}\) and \((B_{m,n})_{m,n \in\mathbb{N}_0}\) of bivariate (tensor product) Baskakov and Baskakov-Kantorovič operators are known to form a pointwise approximation process on spaces of continuous functions \(f\) in two variables with \(w_{p,q}f\) uniformly continuous and bounded on \([0,\infty) \times [0,\infty)\), where \(w_{p,q}(x,y): =(1+x^p)^{-1} (1+y^q)^{-1}\), \(p,q\in\mathbb{N}_0\). Assuming additionally \(C^2\)-smoothness and \(C^1\)-smoothness respectively the authors prove a pointwise Voronovskaja type result (Theorem 3) and the pointwise convergence of the partial derivatives of \(A_{m,n}f\) and \(B_{m,n}f\) to the corresponding partial derivative of \(f\) (Theorem 4).
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 1454847
zbMATH Keywords: Baskakov operators
zbMATH Keywords: weighted function spaces
zbMATH Keywords: bivariate operators
zbMATH Keywords: Baskakov-Kantorovič operators
reviewed by: Manfred Wolfgang Müller
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1454847