Posts by Octavian Agratini

Abstract


We propose a general class of polynomials investigating the convergence of the operators constructed on the basis of these polynomials. The estimate of the error is given in terms of the modulus of continuity. Special examples are delivered

Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Durrmeyer operator; self-adjoint operator; Lebesgue space

Paper coordinates

O. Agratini, A generalization of Durrmeyer-type polynomials and their approximation, Applications of Fibonacci Numbers, Proceedings of the tenth international research conference on Fibonacci numbers and their applications, 9 (2004), pp. 9-18.

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[1] Abramowitz, M., Stefun, I.A., Handbook of Mathematical Funcitons with Formuls,  Graphs and Mathematical Tables,  National Bureau of Standards Applied Mathematics Series, vol. 55, Issued June, 1964.
[2] Altomare, F., Campiti, M., Korovkin-type Approximation Theory and its Applicaitons, de Gruyer Studies in Mathematics, vol. 17 de Gruyter, Berlin, New York, 1964.
[3] Cmpiti, M., Metafune, G., Approximation Properties of Recursively Defined Bernstein-Type Operators,  J. Approx. Theory, vol. 87 (1996), pp., 243-269.
[4] Derriennic, M.M., Sur l’approximation de fonctions integrables sur [0,1] par des polynomes de Bernstein modifies, J. Approx. Theory, vol. 31 (1981), pp. 325-343.
[5] Durrmeyer, J.L., Une formule d’inversion de la transformee de Laplace: Applications a la theorie des moments, These de 3e cycle, Faculte des Sciiences de l’Universite de Paris, 1967.
[6] Jurkat, W.B., Lorentz, G.G., Uniform approximation by Polynomials with Positive Coefficients, Duke Math. J., vol. 28(1961), pp. 463-474.

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