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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

On approximation of functions by means of Weierstrass theorem

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pp. 963–970Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-2075XML
Received:
15 Oct 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2075
Pages:
963–970

Abstract

This aims to study and analyze the approximation of the functions in the space Lp by utilizing the Means of Weierstrass theorem by using Bernstein polynomial, Jackson operator, Fejer operator and Landau operator respectively. The goal is to determine which one is better in the approximating functions. 

Keywords

Subject Classifications

Primary 93A30Secondary 49K15

References

[1] I. P. Natanson, Constructive Function Theory Volume I: Uniform Approximation. New York, NY, USA: Frederick Ungar Publishing Co. (1964).
[2] K. H. Khalaf, M. M. Al-Janabi, A. M. Abdulwahid, and M. H. Jabbar, “Study of some properties for pre measure,” AIP Conf. Proc., vol. 2834, no. 1 (2023), doi: 10.1063/5.0162036.
[3] S. Ostrovska, “The first decade of the q-Bernstein polynomials: Results and perspectives,” J. Math. Anal. Approx. Theory, vol. 2, pp. 35–51 (2007).
[4] A. H. Zaboon and S. Al-Saidy, “Multiplier approximation of functions by q-Bernstein-Kantorovich operator,” J. Phys. Conf. Ser., vol. 1897, p. 012055 (2021), doi: 10.1088/1742-6596/1897/1/012055.
[5] O. Eidous and J. Abu-Hawwas, “An accurate approximation for the standard normal distribution function,” J. Inf. Optim. Sci., vol. 42, no. 1, pp. 17–27 (2019).
[6] A. G. Babenko, “One-sided approximation in L1L^1L1 of the characteristic function of an interval by trigonometric polynomials,” Tr. Inst. Mat. Mekh., vol. 18, no. 1, pp. 88–95 (2012).
[7] A. H. Zaboon and S. Al-Saidy, “Approximation of unbounded functions by positive linear operators in locally-global weighted spaces,” Int. J. Math. Arch., vol. 5, no. 4, pp. 1–9 (2014).
[8] G. M. Phillips, Interpolation and Approximation by Polynomials (CMS Books in Mathematics). New York, NY, USA: Springer (2003).
[9] G. G. Lorentz, Bernstein Polynomials. New York, NY, USA: Chelsea Publishing Company, pp. 1–134 (1986).
[10] S. K. Al-Saidy, N. J. Al-Jawari, and A. H. Zaboon, “Best multiplier approximation of unbounded periodic functions in Lφnp(B)L^p_{\varphi_n}(B)Lφnp(B), B=[0,2π]B = [0,2\pi]B=[0,2π], using discrete linear positive operators,” Baghdad Sci. J., vol. 17, no. 3, pp. 882–888 (2020).
[11] A. H. Zaboon, “Approximation of functions in the Lwp(X)L^p_w(X)Lwp(X)-space and applications,” J. Interdiscip. Math., vol. 26, no. 4, pp. 715–723 (2023).
[12] V. K. Dzyadyk, Theory of Uniform Approximation of Functions by Polynomials. Berlin, Germany: Walter de Gruyter (2008).
[13] H. Werner, Über Approximations Theorie. Berlin, Germany: Springer-Verlag (2008).

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