The generalization of bivariate MKZ operators by multiple generating functions
type: Item
instance of: scholarly article
title: The generalization of bivariate MKZ operators by multiple generating functions
zbMATH Open document ID: 1119.41019
author: Fatma Taşdelen
author: Ayşegül Erençin
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-05-04T00:00:00Z
review text: In \textit{J. Altin}, \textit{O. Doğru} and \textit{F. Taşdelen} [J. Math. Anal. Appl. 312, No. 1, 181--194 (2005; Zbl 1076.41008)] it is introduced for functions \(f: [0,1)\to \mathbb{R}\) a sequence of linear positive operators defined by \[ L_n(f, x)={1\over h_n(x, t)} \sum^\infty_{k=0} f\Biggl({a_{k,n}\over a_{k,n}+ b_n}\Biggr) c_{k,n}(t) x^k,\quad x\in [0,1), \] where \(0\leq{a_{k,n}\over a_{k,n}+ b_n}\leq A\), \(A\in (0,1)\), and \(\{h_n(x, t)\}\) is the generating functions for the sequence of functions \(\{c_{k,n}(t)\}\) in the form \[ h_n(x, t)= \sum^\infty_{k=0} c_{k,n}(t) x^k \] for all \(t\in I\) (\(I\) is an arbitrary subinterval of \(\mathbb{R})\). In the present paper is considered the bivariate version of the operators \(L_n\). Some Korovkin-type approximation properties of these bivariate operators are established and applications to partial differential equations are given.
reviewed by: Zoltán Finta
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 5149593
zbMATH Keywords: positive linear operators
zbMATH Keywords: Volkov type theorem
zbMATH Keywords: bivariate Meyer-König and Zeller operators
zbMATH Keywords: modified Lipschitz class
zbMATH Keywords: modulus of continuity
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.09.024
OpenAlex ID: W1995898647
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DOI: 10.1016/J.JMAA.2006.09.024
description: scientific article; zbMATH DE number 5149593