Some approximation results on Bernstein-Schurer operators defined by ( p , q ) $(p,q)$ -integers

Abstract

Recently, Mursaleen et al. (On $(p,q)$ -analogue of Bernstein operators, arXiv:1503.07404 ) introduced and studied the $(p,q)$ -analog of Bernstein operators by using the idea of $(p,q)$ -integers. In this paper, we generalize the q-Bernstein-Schurer operators using $(p,q)$ -integers and obtain a Korovkin type approximation theorem. Furthermore, we obtain the convergence of the operators by using the modulus of continuity and prove some direct theorems.