Abstract


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.

Authors

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

Keywords

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

Paper coordinates

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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About this paper

Journal

Facta Universitatis

Publisher Name

University of Nis

Print ISSN
0352-9665
Online ISSN

2406-047X

google scholar link

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2. W. Feller: An Introduction to Probability Theory and its Applications I,II. John Wiley, New-York, 1957. resp. 1966.
3. H. H. Gonska and J. Meier: Quantitative theorems on approximation by Bernstein-Stancu operators. Calcolo 21 (1984),4,317-335.
4. A. Lupas¸: The approximation by some positive linear operators. In: Proceedings of the International Dortmund Meeting on Approximation Theory (M.W. Muller et al., eds.), Akademie Verlag, Berlin, 1995, pp. 201-229.
5. M. M. Rao: Probability Theory with Applications. Academic Press, New York, 1984.
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.

1999

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