Bezier variant of modified α-Bernstein operators

In the present paper, we introduce the Bezier variant of modified alpha-Bernstein operators and study the degree of approximation using second order modulus of continuity. We also establish a direct approximation theorem with the aid of Ditzian-Totik modulus of smoothness and the Peetre's K-functional. Further, we obtain a quantitative Voronovskaja type theorem and the rate of convergence for functions with a derivative of bounded variation on [0, 1]. Finally, we depict the rate of convergence of these operators for certain functions by graphical illustration using Matlab software.