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

The rates of convergence of two Bernstein–Bézier type operators B(α)n and L(α)n for functions of bounded variation have been studied for the case α⩾1 by the author and A. Piriou (1998, J. Approx. Theory95, 369–387). In this paper the other case 0<α<1 is treated and asymptotically optimal estimations of B(α)n and L(α)n for functions of bounded variation are obtained. Besides, some interesting behaviors of the operators B(α)n and L(α)n (α>0) for monotone functions and functions of bounded variation are also given.