On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions Original Research Article

In this paper we study the rate of convergence of two Bernstein–Bézier type operatorsB(α)nandL(α)nfor bounded variation functions. By means of construction of suitable functions and the method of Bojanic and Vuillemier (J. Approx. Theory31(1981), 67–79), using some results of probability theory, we obtain asymptotically optimal estimations ofB(α)nandL(α)nfor bounded variation functions at points of continuity and points of discontinuity.