Some approximation results for the Bézier variants of two generalized Bernstein type operators

In this paper we introduce two new B?zier variants of the generalized Bernstein type operators. With the help of Ditzian Totik smooth modulus, we discuss a global approximation. Also, we obtain the rate of convergence of the operators by the second order continuous modulus and Peetre K-functional. By using the construction of appropriate functions and the methods of Bojanic-Cheng, the approximation properties of the new defined operators for absolute continuous functions with derivatives equivalent to bounded variation functions is given. Finally, we provide four graphs to illustrate the approximation effect of the newly defined operators.