Inverse theorem for the Szász-Durrmeyer operators

Authors

  • Tomasz Świderski Pedagogical University, Krakow, Poland

DOI:

https://doi.org/10.33993/jnaat382-914

Keywords:

Modified Szász-Mirakyan operator, Baskakov-Durremeyer operator
Abstract views: 243

Abstract

In the present paper we establish direct and inverse local properties for the Szász-Durrmeyer operators. These operators are introduced in [1] and independently considered in [4] as the generalized integral operators proposed by S.M. Mazhar and V. Totik in [2].

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References

Ciupa, A. and Gavrea, I., On a modified Favard-Szasz operator, Univ. Babeş-Bolyai, Cluj-Napoca, Faculty of Math. and Informatics Research Seminars, Seminar on Numerical and Statistical Calculus, 1, pp. 39-44, 1994.

Mazhar, S.M. and Totik, V., Approximation by modified Szász operators, Acta Sci. Math. (Szeged) 49, pp. 364-383, 1985.

Li, S., Local Smoothness of Functions and Baskakov-Durrmeyer Operators, J. Approx. Theory, 88, pp. 139-156, 1997, https://doi.org/10.1006/jath.1996.3016 DOI: https://doi.org/10.1006/jath.1996.3016

Świderski, T., Global approximation theorems for the generalized modified Szász-Mirakyan operators in polynomial weight spaces, Demonstr. Math., XXXVI, No. 2, pp. 395-404, 2003. DOI: https://doi.org/10.1515/dema-2003-0213

Wachnicki, E., On a Gauss-Weierstrass generalized integral, Akad. Ped. Kraków Rocznik Nauk.-Dydakt., 204, Prace Matematyczne 17, pp. 251-263, 2000.

Zhou, D.-X., On a paper of Mazhar and Totik, J. Approx. Theory, 72, pp. 290-300, 1993, https://doi.org/10.1006/jath.1993.1023 DOI: https://doi.org/10.1006/jath.1993.1023

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Published

2009-08-01

How to Cite

Świderski, T. (2009). Inverse theorem for the Szász-Durrmeyer operators. Rev. Anal. Numér. Théor. Approx., 38(2), 182–190. https://doi.org/10.33993/jnaat382-914

Issue

Vol. 38 No. 2 (2009)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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