On the Remainder Term of Some Bivariate Approximation Formulas Based on Linear and Positive Operators

Year 2018, Volume: 1 Issue: 2, 73 - 87, 07.11.2018

Dan Bărbosu

https://doi.org/10.33205/cma.442151

Cited By: 6

Abstract

The paper is a survey concerning representations for the remainder term of Bernstein-Schurer-Stancu and respectively Stancu (based on factorial powers) bivariate approximation formulas, using bivariate divided differences. As particular cases the remainder terms of bivariate Bernstein-Stancu, Schurer and classical Bernstein bivariate approximation formulas are obtained. Finally, one presents some mean value properties, similar to those of the remainder term of classical Bernstein univariate approximation formula.

Keywords

Bernstein-Schurer-Stancu bivariate operator, Stancu bivariate operator, Bivariate divided difference, Bivariate approximation formula, Remainder term

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