Durrmeyer-Stancu type operators

Authors

  • Ovidiu T. Pop National College "Mihai Eminescu", Satu Mare
  • Dan Bărbosu North University of Baia Mare

Keywords:

linear positive operators, Durrmeyer operators, first order modulus of smoothness, Shisha-Mond theorem

Abstract

Considering two given real parameters \(\alpha, \beta\) satisfying the conditions \(0\leq\alpha\leq\beta\), D. D. Stancu [7] constructed and studied the linear positive operators \(P^{(\alpha,\beta)}_m:C([0,1])\to C([0,1])\), defined for any \(f\in C([0,1])\) and any positive integer \(m\) by (1). In this paper we are dealing with the Durrmeyer form of Stancu's operators. Some approximation properties of these Durrmeyer-Stancu operators are established. As a particular case, we retrieve approximation properties for the classical Durrmeyer operators [5].

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References

O. Agratini, Aproximare prin operatori liniari, Presa Universitară Clujeană, Cluj-Napoca, 2000 (in Romanian).

F. Altomare and M. Campiti, Korovkin-type Approximation Theory and its Applications, de Gruyter, Series Studies in Mathematics, 17, Walter de Gruyter&Co, Berlin, New-York, 2000.

D. Bărbosu, Durrmeyer-Schurer type operators, Facta Univ. (Nis), Ser. Math-Inform., 19, pp. 65-72, 2004.

S.N. Bernstein, Demonstration du théorème de Weierstrass fondeé sur le calcul des probabilités, Commun. Soc. Math. Kharkhov, 13(2), pp. 1-2, 1912-1913.

J.L. Durrmeyer, Une formule d'inversion de transformée de Laplace: Application à la theorie des moments, Thèse de 3e cycle, Faculté de Sciences de l'Université de Paris, 1967.

O. Shisha and B. Mond, The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. U.S.A, 60, pp. 1196-2000, 1968, https://doi.org/10.1073/pnas.60.4.1196

D.D. Stancu, Asupra unei generalizări a polinoamelor lui Bernstein, Studia Univ. "Babeş-Bolyai", 14(2), pp. 31-45, 1969 (in Romanian).

D.D. Stancu, Gh. Coman, O. Agratini, R. Trimbiţaş, Analiză Numerică şi Teoria Aproximării, I, Presa Universitară Clujeană, Cluj-Napoca, 2001 (in Romanian).

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Published

2010-08-01

How to Cite

Pop, O. T., & Bărbosu, D. (2010). Durrmeyer-Stancu type operators. Rev. Anal. Numér. Théor. Approx., 39(2), 150–155. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2010-vol39-no2-art6

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