The purpose of this paper is to study a sequence of linear and positive operators which was proposed by A. Lupas . 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.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Lupas operator; Bohman-Korovkin theorem; Voronovskaya-type formula; uniform approximation
O. Agratini, On a sequence of linear and positive operators, Facta Universitatis, Nis, Series: Mathematics and Informatics, 14 (1999), pp. 41-48.
University of Nis
google scholar link
1. F. Altomare and M. Campiti: Korovkin-Type Approximation Theory and its Applications. de Gruyter Series Studies in Mathematics, Vol. 17, Walter de Gruyter, Berlin, New-York, 1994.
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.