Jacobi Weighted Moduli of Smoothness for Approximation by Neural Networks Application

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Eman S. Bhaya
Najlaa A. Hadi

Abstract

          Moduli of smoothness are intended for mathematicians working in approximation theory, numerical analysis and real analysis. Measuring the smoothness of a function by differentiability is two grade for many purposes in approximation theory. More subtle measurement are provided by moduli of smoothness.


Many versions of moduli of smoothness and  K-functionals introduced by many authors. In this work we choose two of these moduli and prove that they are equivalent themselves once and with a version of K-functional twice, under certain conditions.


As an application of our work we introduce a version of Jackson theorem for the approximation by neural networks.

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How to Cite
[1]
“Jacobi Weighted Moduli of Smoothness for Approximation by Neural Networks Application”, JUBPAS, vol. 28, no. 3, pp. 121–134, Dec. 2020, Accessed: Mar. 29, 2024. [Online]. Available: https://journalofbabylon.com/index.php/JUBPAS/article/view/3362
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How to Cite

[1]
“Jacobi Weighted Moduli of Smoothness for Approximation by Neural Networks Application”, JUBPAS, vol. 28, no. 3, pp. 121–134, Dec. 2020, Accessed: Mar. 29, 2024. [Online]. Available: https://journalofbabylon.com/index.php/JUBPAS/article/view/3362

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