Approximation using a modified type of Bernstein operators

Abstract

A new generalization for the Bernstein-Kantorovich operator with a parameter is proposed in this study. First, we prove the Korovkin type approximation theorem, then we provide the Voronovskaja type theorem for our generalization, demonstrating that the order of approximation is improved, making the approximation by our operators better than the original Kantorovich, and finally, we provide some numerical data for two test functions to support the study.