An extension of the Cheney-Sharma operator of the first kind

Authors

  • Teodora Cătinaș Babeș-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania
  • Iulia Buda Babeș-Bolyai University, Faculty of Mathematics and Computer Science & Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania https://orcid.org/0000-0003-3820-3869

DOI:

https://doi.org/10.33993/jnaat522-1373

Keywords:

Cheney-Sharma operator, Stancu operator, modulus of smoothness, Lipschitz function
Abstract views: 99

Abstract

We extend the Cheney-Sharma operators of the first kind using Stancu type technique and we study some approximation properties of the new operator. We calculate the moments, we study local approximation with respect to a K-functional and the preservation of the Lipschitz constant and order.

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References

O. Agratini, Approximation by linear operators, Cluj University Press, 2000.

G. Bascanbaz-Tunca, A. Erencin, F. Tasdelen, Some properties of Bernstein type Cheney and Sharma Operators, General Mathematics, 24 (2016), pp. 17-25.

E.W. Cheney, A. Sharma, On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma, 2 (1964), pp. 77-84.

T. Bostanci, G. Bascanbaz-Tunca, A Stancu type extension of Cheney and Sharma operator, J. Numer. Anal. Approx. Theory, 47 (2018), pp. 124-134, https://doi.org/10.33993/jnaat472-1133. DOI: https://doi.org/10.33993/jnaat472-1133

D.D. Stancu, C. Cismasiu, On an approximating linear positive operator of Cheney-Sharma, Rev. Anal. Numer. Theor. Approx., 26 (1997), pp. 221-227.

D.D. Stancu, Quadrature formulas constructed by using certain linear positive operators, Numerical Integration (Proc. Conf., Oberwolfach, 1981), ISNM 57 (1982), pp. 241-251, https://doi.org/10.1007/978-3-0348-6308-7_23. DOI: https://doi.org/10.1007/978-3-0348-6308-7_23

D.D. Stancu, G. Coman, O. Agratini, R.T. Trımbitas, , P. Blaga, I. Chiorean, Analiza numerica și teoria aproximarii, Presa Universitara Clujeana, 2001 (in Romanian)

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Published

2023-12-28

How to Cite

Cătinaș, T., & Buda, I. (2023). An extension of the Cheney-Sharma operator of the first kind. J. Numer. Anal. Approx. Theory, 52(2), 172–181. https://doi.org/10.33993/jnaat522-1373

Issue

Vol. 52 No. 2 (2023)

Section

Articles

License

Copyright (c) 2023 Teodora Catinas, Iulia Buda

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.