The purpose of this paper is to study a sequence of linear and positive operators which was proposed by A. Lupas [4]. An asymptotic formula and some quantitative estimates for the rate of convergence are given. By using a probabilistic method,this sequence is reobtained. Also two modified sequences are constructed.


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


Lupas operator; Bohman-Korovkin theorem; Voronovskaya-type formula; uniform approximation

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O. Agratini, On a sequence of linear and positive operators, Facta Universitatis, Nis, Series: Mathematics and Informatics, 14 (1999), pp. 41-48.


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Facta Universitatis

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University of Nis

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6. D.D. Stancu: Use of probabilistic methods in the theory of uniform approximation of continuous functions. Rev. Roum. Math. Pures et Appl. 14 (1969),5,673-691.


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