On the rate of convergence of the Bézier type operators (Q5933544)

For locally bounded functions, the degree of pointwise approximation by means of the Bézier type modification of some discrete Feller operators is investigated. In particular, corresponding results for functions of bounded \(p\)-th power variation are deduced. The estimates are given in terms of a modulus of variation considered previously by \textit{Z. A. Chanturija} [Dokl. Akad. Nauk SSSR 214, 63-66 (1974; Zbl 0295.26008)] and are too involved to be reproduced here. Finally, applications of the main results for the Bézier type modification of some well-known positive linear operators are presented.