Home 9 Volume 9 Parametrized error function based Banach space valued univariate neural network approximation
Open AccessArticle
Parametrized error function based Banach space valued univariate neural network approximation

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

* Corresponding Author
Annals of Communications in Mathematics 2023
, 6 (1),
31-43.
https://doi.org/10.62072/acm2023060104
Received: 30 Jan 2023 |
Accepted: 28 Feb 2023 |
Published: 31 Mar 2023

Abstract

Here we research the univariate quantitative approximation of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. We perform also the related Banach space valued ractional approximation. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative or fractional derivaties. Our operators are defined by using a density function induced by a parametrized error function. The approximations are pointwise and with respect to the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer. We finish with a convergence analysis.

Keywords

Cite This Article

Parametrized error function based Banach space valued univariate neural network approximation.

Annals of Communications in Mathematics,

2023,
6 (1):
31-43.
https://doi.org/10.62072/acm2023060104
  • Creative Commons License
  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

    0 Comments

    Submit a Comment

    Your email address will not be published. Required fields are marked *

    Preview PDF

    XML File

    Loading

    Share