Approximation properties of generalized Kantorovich–Schurer–Stancu operators

In this paper, we introduce generalized Bernstein–Kantorovich-type operators with two shifted notes and study their approximation properties. First, we calculate some estimates for these operators. Further, we discuss convergence theorems and order of approximation in terms of Korovkin theorem and first-order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetre’s K-functional, second-order modulus of smoothness, Lipschitz-type space and [Formula: see text]th order Lipschitz-type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.