Bézier–Bernstein–Durrmeyer type operators

In this note, we construct the Bézier variant of the Bernstein–Durrmeyer type operators. We present local results, a direct approximation theorem by using the Ditzian–Totik modulus of smoothness and a quantitative Voronovskaja type theorem with the help of the Ditzian–Totik modulus of continuity. The rate of convergence for differential functions whose derivatives are of bounded variation is also established. Finally, we show that the numerical examples which illustrate the authenticity of the theoretical results and the effectiveness of the defined operators.