Abstract
We present a new probabilistic method for constructing a sequence of linear positive operators
used in uniform approximation of the continuous functions of two variables.
We study the convergence of the sequence and we evaluate the approximation order.
Finally, we present some examples which extend the results obtained in [2] to the case of two variables.
Authors
Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
bidimensional linear positive operator; probability space; order of approximation; modulus of continuity
Paper coordinates
O. Agratini, On the construction of approximating linear positive operators by probabilistic methods, Studia Univ. “Babes-Bolyai”, Mathematica, 38 (1993) no. 4, pp. 45-50.
About this paper
Journal
Studia Universitatis “Babes-Bolyai” Mathematica
Publisher Name
DOI
Print ISSN
1843-3855
Online ISSN
2065-9490
1843-3855
google scholar link
[1] Chency, E.W. and Sharma, A., On a generaization of Bernstein polynomials, Rev. Mat. Univ. Parma (2), 5 (1964), 77-84.
[2] Jain, G.C. and Pethe, S., On a generalization of Bernstein and Szasz Mirakyan operators, Nanta Mathematica, vol. X (2), 185-194.
[3] King, J.P., Probabilistic analysis of Korokvin’s theorem, Journal of the Indian Math. Soc., 44(1980), 51-58.
[4] Khan, R.A., Some probabilistic methods in the theory of approximation operators, Acta Mathematica Academiae Scientiarum Hungaricae, 35 (1-2), 1980, 193-203.
[5] Korokvin, P.P., Linear operators and approximation theory, Hindustan Publ. Corp., Delhi, 1960.
[6] Muller, M., Die folge der Gammaoperatoren, Dissenation, Stuttgart, 1967.
[7] Razi, Quasim, Approximation of a function by Kantorovich type operators, Matematicki Vesnik, 41 (1989), 183-192.
[8] Stancu, D.D., Approximation of functions by a new class of linear poly operators, Revue Doumaine de Math. Pures et Appl., 13 (1968), 1173-1194.
[9] Stancu, D.D., Use of probabilistic methods in the theory of uniform approximation of continuous functions, Revue Roumaine de Math Pures et Appl., 14(1969), 673-691.
[10] Stancu, D.D., Approximation of funcitons by means of a new heneralized Bernstein operator, Calcolo, vol. XX, fasc. II, 1983, 211-229.