Abstract
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.
Authors
Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Bernstein-type operator; Stancu operator; Kantorovich operator; rate of convergence
Paper coordinates
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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