Rate of convergence for the Bézier variant of the Bleimann--Butzer--Hahn operators (Q812755)

A very interesting and nice result concerning some approximation properties for the Bézier variant of the Bleimann-Butzer-Hahn operators is established. More exactly, the rate of convergence for the above operators in terms of total variation of approximated function is expressed (this is the main result of the paper). The proof is based upon four lemmas, where the properties of Stirling numbers of second kind, the properties of Bernstein basis functions and the Markov's inequality are essentially used.