An estimation on the rate of convergence for modified Beta operators. (Q1432767)

The authors consider linear combinations \(B_n\), \(n\in\mathbb{N}\) of slightly modified Beta operators of Durrmeyer type defined for continuous functions \(f\) on \([0,\infty)\) with polynomial growth and study the approximation of \((B_nf)^{(r)}\) to \(f^{(r)}\) (provided \(f^{(r)}\) exists on \([0,\infty)\) and is of polynomial growth as well). The main result is a local estimate of the error in terms of classical higher-order local moduli of smoothness. The paper contains a lot of very disagreeable misprints.