On the Durrmeyer-type modification of some discrete approximation operators

In [10], for continuous functionsf from the domain of certain discrete operatorsL _n the inequalities are proved concerning the modulus of continuity ofL _nf. Here we present analogues of the results obtained for the Durrmeyer-type modification $tilde L_n $ ofL _n. Moreover, we give the estimates of the rate of convergence of $tilde L_n f$ in Hölder-type norms