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

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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