Higher order \(\alpha \)-Bernstein–Kantorovich operators

In this paper, we discuss the higher-order \(\alpha \) $\alpha$ -Bernstein–Kantorovich operators, which are associated with the Bernstein polynomials. We analyze various aspects, such as error estimations and Voronovskaja-type asymptotic formula. Finally, we provide a comparative study by visualizing the results graphically and interpreting the upper limit of the error numerically.