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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 10, 2017

The Voronovskaja type theorem for an extension of Szász-Mirakjan operators

  • Ovidiu T. Pop EMAIL logo , Dan Bărbosu and Dan Miclăuş
From the journal Demonstratio Mathematica

Abstract

Recently, C. Mortici defined a class of linear and positive operators depending on a certain function ϕ, which generalize the well known Szász-Mirakjan operators. For these generalized operators we establish a Voronovskaja type theorem, the uniform convergence and the order of approximation, using the modulus of continuity.

MSC 2010: 41A10; 41A25; 41A36

References

[1] O. Agratini, Approximation by linear operators (in Romanian), Presa Universitară Clujeană, Cluj-Napoca 2000.Search in Google Scholar

[2] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its Applications, de Gruyter Series Studies in Mathematics, 17, Walter de Gruyter & Co., Berlin, New York 1994.10.1515/9783110884586Search in Google Scholar

[3] J. Favard, Sur les multiplicateurs d’interpolation, J. Math. Pures Appl. 23(9) (1944), 219–247.Search in Google Scholar

[4] A. Jakimovski, D. Leviatan, Generalized Szász operators for the approximation in the infinite interval, Mathematica (Cluj) 34 (1969), 97–103.Search in Google Scholar

[5] G. M. Mirakjan, Approximation of continuous functions with the aid of polynomials (in Russian), Dokl. Acad. Nauk. SSSR 31 (1941), 201–205.Search in Google Scholar

[6] C. Mortici, An extension of the Szász-Mirakjan operators, An. St. Univ. Ovidius Constanţa 17(1) (2009), 137–144.Search in Google Scholar

[7] O. T. Pop, About some linear and positive operators defined by infinite sum, Demonstratio Math. 39 (2006), 377–388.Search in Google Scholar

[8] O. Szász, Generalization of S. N. Bernstein’s polynomials to the infinite interval, J. Research, National Bureau of Standards 45 (1950), 239–245.10.6028/jres.045.024Search in Google Scholar

Received: 2010-10-12
Published Online: 2017-5-10
Published in Print: 2012-3-1

© 2012 Ovidiu T. Pop et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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