Posts by Octavian Agratini


In this paper we consider an extension, in the sense of Kantorovich, of a linear positive operator of Bernstein type \(L_{m,r}^{\alpha,\beta}\), introduced by D.D. Stancu in the paper [7]. For this extension we establish some quantitative theorems representing estimaitons of the orders of approximation, by using the first and the second orders modulus of continuity. Also we give an asymptotic estimation, in the sense of Voronovskaja.


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


Bernstein-type operator; Stancu operator; Kantorovich operator; rate of convergence

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O. Agratini, Approximation  properties of a class of operators of Stancu-Kantorovich type, Research Seminar on Numerical and Statistical Calculus, “Babes-Bolyai” Univ., Cluj-Napoca, 1 (1994), pp. 3-12.


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“Babes-Bolyai” University, Faculty of Mathematics and Computer Science

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[1] Gonsca, H.H., On approximation of continuosly differentiable fumnctions by positive linear operators,  Bull. Austral. Math. Soc., 27(1983), 73-81.
[2] Gonska, H.H., On approximation by linear operators improved estimates,  Revue d’Analyse Numerique et de Theorie de l’Approximaiton, 14(1985), no.1, 7-32.
[3] Gonsca, H.H., Meier, J., Quantitative theorems an approximation by Bernstein-Stancu operators,  Calcolo, vol. XXI, fsc. IV, 1984, 317-335.
[4] Derriennic, M.M., Sur l’approximaiton de fonctions integrables sur [0,1] par des polynomes de Bernstein modifies,  Journal of Approximation Theory, 31(1981), 325-343.
[5] Lorentz, G.G., Bernstein Polynomiasl, University of Toronto Press, Toronto, 1953.
[6] Stancu, D.D.,  Use of probabilistic methods in the theory of uniform approximation of continuous functions,  Rev. Roumaine Math. Pures Appl., 14(1969), 673-691.
[7] Stancu, D.D.,  Approximation of functions by menas of a new generalized Bernstein Operator,  Calcolo, vol.XII, fasc. 11, 1983, 211-229.

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