Some properties of the generalized Favard-Durrmeyer operators

Abstract

The Durrmeyer modification $\tilde{F}_{n}f$ of the generalized Favard operators in some weighted function spaces are considered. The rate of convergence of $\tilde{F}_{n}f(x)$ at the Lebesgue points $x$ of $f$ is estimated. In particular, a corresponding estimate in the class of functions $f$ of bounded $p$-th power variation is deduced.