Abstract In this paper we introduce a Stancu–Schurer type extension of higher order of the Cheney–Sharma operators. Starting from the operators studied by Bostanci and Başcanbaz-Tunca, respectively by Cătinaş and Buda (in the form of a Stancu operator with generalized Bernstein polynomials) we extend the convex combination of two terms which appears in the expression of the operator to a convex combination of m terms, where m ∈ N m N, with m ≥ 1. We called these new operators the Stancu–Schurer type extension of order m of the Cheney–Sharma operators (of first, respectively second kind). For these operators we study some approximation and convexity properties, modulus of continuity and Korovkin-type theorems.
Grigoriciuc et al. (Tue,) studied this question.