On (p, q)-analogue of modified Bernstein–Schurer operators for functions of one and two variables

Abstract

In this paper, we introduce a new kind of modified Bernstein–Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Next, we construct the bivariate operators and get some convergence properties. Finally, we give some graphs to illustrate the convergence properties of operators to some functions.