Jacobi Weighted Moduli of Smoothness for Approximation by Neural Networks Application

Authors

  • Eman S. Bhaya Mathematics Department, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq
  • Najlaa A. Hadi Computer Sciences Department, College of Sciences for Girls, University of Babylon, Babylon, Iraq

Keywords:

Jacobi modulus of smoothnessn, Neural networks, Best approximation, Modulus of smoothness.

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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Published

2020-12-31

How to Cite

[1]
E. S. . Bhaya and N. A. . Hadi, “Jacobi Weighted Moduli of Smoothness for Approximation by Neural Networks Application”, JUBPAS, vol. 28, no. 3, pp. 121-134, Dec. 2020.

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Articles