The first absolute moment for some operators

Authors

  • Ovidiu T. Pop National College "Mihai Eminescu", Satu Mare
  • Petru I. Braica Secondary School "Grigore Moisil", Satu Mare

Keywords:

Bernstein's polynomials, Szász-Mirakjan operators, Bleimann-Butzer-Hahn operators, Meyer-Konig and Zeller operators, absolute moment of high order

Abstract

In this paper we will determinate the first absolute moments for Bernstein, Szász-Mirakjan, Bleimann-Butzer-Hahn, Meyer-König and Zeller operators. For the Szász-Mirakjan operators we give some properties with the absolute moment of high order.

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References

M. Beker and R.J. Nessel, A global approximation theorem for Meyer-König and Zeller opeators, Math. Zeitschr., 160, pp. 195-206, 1978, https://doi.org/10.1007/bf01237033

G. Bleimann, P.L.. Butzer and L.A. Hahn, Bernstein-type operator approximating continuous fucntion on the semi-axix, Indag. Math., 42, pp. 255-262, 1980, https://doi.org/10.1016/1385-7258(80)90027-x

S.N. Bernstein, Démonstration fu théorème de Weierstrass fondée sur le calcul de probabilité, Commun. Soc. Math. Kharkow (2), 13, pp. 1-2, 1912-1913.

J. Favard, Sur les multiplicateurs d'interpolation, J. Math. Pures Appl., (9), 23, pp. 219-247, 1994.

J. Meier, Zur Approximation durch gewöhnliche und modifizierte Bernstein-Operatoren unter besonderer Berücksichtigung quantitaver Aussagen und asymtotischer Formeln, Staatsexamensarbeit, Unviersität Duisburg, 1982.

W. Meyer-König and K. Zeller, Bernsteinsche Potenzreihen, Studia Math., 19, pp. 89-94, 1960, https://doi.org/10.4064/sm-19-1-89-94

G.M. Mirakjan, Approximation of continuous functions with the aid of polynomials, Dokl, Acad. Nauk SSSR, 31, pp. 201-205, 1941 (in Russian).

M.W. Müller, Die folge der Gammaoperatoren, Dissertation, Stutgart, 1967.

O.T. Pop, About the first order modulus of smoothness, Caprathian J. Math., 20, pp. 101-108, 2004.

F. Schurer and F.W. Steutel, On the degree of approximation of fucntions in C¹([0,1]) by Bernstein polynomials, T.H. Report 75-WSK-07, Eindhoven University of Technology, 1975.

D. D. Stancu, Gh. Coman, O. Agratini and R. Trîmbiţaş, Numerical analysis and approximation theory, I. Cluj, University Press, Cluj-Napoca, 2001, (in Romanian).

O. Szász, Generalization of S.N. Bernstein's polynomials to the infinite interval, J. Research, National Bureau of Standards, 45, pp. 239-245, 1950, https://doi.org/10.6028/jres.045.024

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Published

2010-08-01

How to Cite

Pop, O. T., & Braica, P. I. (2010). The first absolute moment for some operators. Rev. Anal. Numér. Théor. Approx., 39(2), 156–163. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2010-vol39-no2-art7

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