Discrete operators associated with the Durrmeyer operator
Keywords:
Positive linear operators, quadrature.Abstract
In [3] the author constructed discrete operators associated with cer- tain integral operators using a probabilistic approach. In this article we obtain positive linear operators of discrete type associated with the classical Durrmeyer operator with the aid of some quadrature formulas with positive coecients. Us- ing 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 linear operators. We study the convergence of the new operators and compare them with the Durrmeyer operator. Also, we present some problems of optimality and give numerical examples.
Mathematics Subject Classification (2010): 41A36.
References
Durrmeyer, J.L., Une formule d'inversion de la transformee de Laplace: applications a la theorie des moments, These de 3e cycle, Faculte des Sciences de l'Universite de Paris, 1967.
Mond, B., Note: On the degree of approximation by linear positive operators, J. Approx. Theory, 18(1976), 304-306.
Rasa, I., Discrete operators associated with certain integral operators, Stud. Univ. Babes-Bolyai Math., 56(2011), no. 2, 537-544.
Stancu, D.D., On a generalization Bernstein polynomials, (in Romanian), Stud. Univ. Babes-Bolyai, 14(1969), 31-45.
Stancu, D.D., Coman, Gh., Blaga, P., Numerical analysis and approximation theory, (in Romanian), vol. II, Presa Universitara Clujeana, 2002.
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