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Symmetry
Volume 16
Issue 8
10.3390/sym16081022
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Article

Degree of Lp Approximation Using Activated Singular Integrals

by
George A. Anastassiou
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA
Symmetry 2024, 16(8), 1022; https://doi.org/10.3390/sym16081022
Submission received: 24 June 2024 / Revised: 10 July 2024 / Accepted: 22 July 2024 / Published: 10 August 2024
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
Versions Notes

Abstract

In this article we present the Lp, p≥1, approximation properties of activated singular integral operators over the real line. We establish their approximation to the unit operator with rates. The kernels here come from neural network activation functions and we employ the related density functions. The derived inequalities use the high order Lp modulus of smoothness.
Keywords: activation functions from neural networks; Lp approximation; singular integral; Lp modulus of smoothness activation functions from neural networks; Lp approximation; singular integral; Lp modulus of smoothness

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MDPI and ACS Style

Anastassiou, G.A. Degree of Lp Approximation Using Activated Singular Integrals. Symmetry 2024, 16, 1022. https://doi.org/10.3390/sym16081022

AMA Style

Anastassiou GA. Degree of Lp Approximation Using Activated Singular Integrals. Symmetry. 2024; 16(8):1022. https://doi.org/10.3390/sym16081022

Chicago/Turabian Style

Anastassiou, George A. 2024. "Degree of Lp Approximation Using Activated Singular Integrals" Symmetry 16, no. 8: 1022. https://doi.org/10.3390/sym16081022

APA Style

Anastassiou, G. A. (2024). Degree of Lp Approximation Using Activated Singular Integrals. Symmetry, 16(8), 1022. https://doi.org/10.3390/sym16081022

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