Abstract
We construct the bivariate form of Bernstein-Schurer operators based on parameter alpha. 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 Bogel differentiable function of our GBS operators is presented.