Approximation of functions by a new class of generalized Bernstein–Schurer operators

Abstract

In this work, we construct a new kind of Bernstein–Schurer operators which includes non-negative real parameter $$\alpha $$ . We study some shape preserving properties, namely, monotonicity and convexity of the new operators. We obtain global approximation formula in terms of Ditzian–Totik uniform modulus of smoothness of first and second order and calculate the local direct estimate of the rate of convergence with the help of Lipschitz-type function for our operators. The Voronovskaja-type approximation theorems of the new operators are presented. Finally, in the last section, we provide some graphs, MATLAB code and numerical examples in order to illustrate the significance of our newly constructed operators.