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Open Access Research Article

Inverse approximation theorem using Bernstein’s Durrmeyer operator in terms of 2nd modulus of smoothness

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pp. 815–819Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1876XML
Received:
12 Dec 2023
Published Online:
30 Jun 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1876
Pages:
815–819

Abstract

Many inverse theorems have been proven using  the ordinary  modulus  of  smoothness but no one proved the invers theorems for approximation by Bernstein’s Durrmeyer operator  in terms 2nd modulus of smoothness.

Keywords

Subject Classifications

14F1041A17

References

[1] H. Johnen, K. Scherer, “On the equivalence of the K-functional and moduli of continuity and some applications”, (Proc. Conf., Math. Res., Springer-Verlag, Berlin–Heidelberg 119–140 (1977).
[2] Z. Ditzian, V. Totik, “Moduli of Smoothness”, SpringerVerlag, New    York, (1987).
[3] H. Berens, Y. Xu,”On Bernstein-Durrmeyer polynomials with Jacobi weights” In: Approximation Theory and Functional Analysis, Academic Press, Boston, pp. 25–46 (1991).
[4] Zhang. Z ,”On weighted approximation by Bernstein-Durrmeyer operators”, Published volume 7, pages 51–64 (1991).
[5] E. Belinsky, E. Liflyand, “Approximation properties in Lp, 0 < p < 1”, Funct. Approx. Comment. Math. 22, 189–199 (1993).
[6] Z. Ditzian, V. Hristov, K. Ivanov,” Moduli of smoothness and K-functional in Lp, 0 < p < 1”, Constr. Approx. 11, 67–83 (1995).
[7] Shunsheng Guo, Gengsheng Zhang Pointwise “Approximation by Bernstein Quasi-interpolants”, Journal of Interdisciplinary Mathematics, Pages 339-349,  Published online: 31 Aug 2006, https://doi.org/10.1081/NFA-120022927.
[8] T. Acar,  A. Aral and V. Gupta, “On approximation properties of a new type of Bernstein-Durrmeyer operators”, Math. Slovaca, 65, 1107-1122 (2015). 
[9] A. M. Acu and P. N. Agrawal, “Better approximation of functions by genuine Bernstein-Durrmeyer type operators”, J. Math. Inequal., 12, 975-987 (2018).  
[10] Q. B. Cai, Ü. D. Kantar and B. Çekim, “Approximation properties for the genuine modified Bernstein-Durrmeyer-Stancu operators”, Appl. Math. J. Chinese Univ. Ser. B, 35, 468-478 (2020).
[11] Yurii Kolomoitsev, Sergey Tikhonov, “Properties of moduli of smoothness in LP(Rd), Journal of Approximation Theory”, Volume 257, September, 105423 (2020).
[12] Zainab Abdulmunim Sharba, Hawraa Abbas Almurieb “Why moduli of p–smoothness”, Journal of Interdisciplinary  Mathematics, Pages 1995-2004 | Received 01 Feb 2021, Published online: 02 Nov (2021), https://doi.org/10.1080/09720502.2021.1964740.
[13] Mohammed Taariq Mowzera, “Convergence in distribution of the Bernstein-Durrmeyer kernel operator”, Department of Mathematics and Applied Mathematics, University of Cape Town, Mathematics (2023), Classical Analysis arXiv:2303.11061.

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