Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators

Abstract

Abstract We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K-functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.

Keywords

• α-Bernstein operators
• Bivariate α-Bernstein–Schurer operators
• GBS operators
• Bögel differentiable function
• Modulus of continuity