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In [3] the author constructed discrete operators associated with certain integral operators using a probabilistic approach. In this article we obtainpositive linear operators of discrete type associated with the classical Durrmeyeroperator with the aid of some quadrature formulas with positive coecients. Using Gaussian quadratures we get operators which preserve the moments of the classical Durrmeyer operator up to a given order. Another class of discrete operators is obtained by using the quadratures generated by some positive linearoperators. We study the convergence of the new operators and compare them with the Durrmeyer operator. Also, we present some problems of optimality andgive numerical examples.

Mathematics Subject Classification (2010): 41A36.

Keywords: Positive linear operators, quadrature.