Have a personal or library account? Click to login
On approximation properties of some non-positive Bernstein-Durrmeyer type operators Cover

On approximation properties of some non-positive Bernstein-Durrmeyer type operators

Open Access
|Feb 2023

References

  1. [1] Acar T., Aral A., Raa I., Modified Bernstein-Durrmeyer operators,General Mathermatics, Vol. 22, 2014.
  2. [2] Adell J.A., J. de la Cal, Bernstein-Durrmeyer operators, Computers & Mathematics with Applications, Volume 30, Issues 36, 1995.10.1016/0898-1221(95)00081-X
  3. [3] Bernstein S. N., Démonstration du théorém de Weierstrass fondeésur la calcul desprobabilitiés. Commun Soc Math Charkow Sér 2(13), 1912
  4. [4] Cheng F., On the rate of convergence of Bernstein polynomials of functions of bounded variation. J Approx Theory 39(3):259-274, 198310.1016/0021-9045(83)90098-9
  5. [5] Deo N., Noor M. A., Siddiqui M.A., On approximation by a class of new Bernstein type operators, Applied Mathematics and Computation, 2008.10.1016/j.amc.2007.12.056
  6. [6] Derriennic M. M., Sur l’approixmation des fonctions integrables sur [0, 1] par des polynomes de Bernstein modifies, J. Approx. Theory, 31, 1981.10.1016/0021-9045(81)90101-5
  7. [7] Durrmeyer J. L., Une formule d’inversion de la transformée de Laplace-applicationsálathéorie des moments,Thése de 3e cycle, Facultédes Science de l’Université de Paris, 1967.
  8. [8] Meleşteu D. A., Generalized Bernstein type operators, Bulletin of the Transilvania University of Braşov, Vol 13(62), No. 2, 2020.10.31926/but.mif.2020.13.62.2.20
  9. [9] Gonska H., On the degree of approximation in Voronovskaja’s theorem. Stud Univ Babe Bolyai Math 52(3):103-115, 2007
  10. [10] Gonska H., Raa I., Asymptotic behaviour of differentiated Bernstein polynomials. Mat Vesnik 61(1):53-60, 2009
  11. [11] Gupta V., Heping W., The rate of convergence of q-Durrmeyer operators for 0 10.1002/mma.1012
  12. [12] Mahmudov N. I., Sabancigil P., On Genuine q-Bernstein-Durrmeyer operators, Academia, 2009.10.5486/PMD.2010.4583
  13. [13] Păltănea R., Approximation theory using positive linear operators. Birkhaüser, Boston, 2004.10.1007/978-1-4612-2058-9
  14. [14] Siddiqui M. A., Agrawal R. R., Gupta N., On a class of modified new Bernstein operators, Adv. Stud. Contem. Math.,(Kyungshang),24, 2014.
  15. [15] Weierstrass, K.G.: U die analytische Darstellbarkeit sogenannter licher Funktionen einer reellen Veranderlichen, Sitzungsber. Akad. Berlin 2, 633-639, 1885.
DOI: https://doi.org/10.2478/auom-2023-0014 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 251 - 269
Submitted on: Mar 19, 2022
Accepted on: Jul 25, 2022
Published on: Feb 4, 2023
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2023 Bianca Ioana Vasian, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.