A note on a Bernstein-type operator of Bleimann, Butzer, and Hahn

Abstract

Let Ln(f, x)(f ε{lunate} C)[0, ∞)) be a Bernstein-type approximation operator as defined and studied by Bleimann, Butzer, and Hahn. Probabilistic arguments are used to simplify and sharpen some of their results. The rates of convergence are given in terms of the first and second moduli of continuity. Moreover, an appropriate limit of Ln is shown to be the well-known Szasz operator. © 1988.