Stancu–Schurer–Kantorovich operators based on q-integers

Abstract

The goal of this paper is to introduce and study q analogue of Stancu–Schurer–Kantorovich operators. A convergence theorem using the well known Bohman–Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. The estimate of the rate of convergence by means of the Lipshitz function is considered. Furthermore, we obtained a Voronovskaja type result for these operators. Also, we investigate the statistical approximation properties of these operators using Korovkin type statistical approximation theorem.