In this paper we are dealing with a general class of linear and positive operators of discrete type. We investigate the convergence of the operators and we give estimates of the rate of convergence by using the classical modulus of continuit, Ditzian-Totik weighted moduli, as well as the weighted K-functional of second order. In some cases we prove that these operators leave invariant the class of increasing funcitons respectively the convex and the Holder continuous funcitons. also a Voronovskaja type formula is established and some concrete exemples are presented.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
linear and positive operator; rate of convergence; Ditzian-Totik weighted modulus; Voronovskaya-type formula
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