Approximation by Steklov Neural Network Operators

TL;DR

This paper introduces a new family of neural network operators called Steklov Neural Network operators, utilizing Steklov integrals to establish convergence properties and rates, advancing approximation theory in neural networks.

Contribution

It presents a novel class of neural network operators based on Steklov integrals, with proven convergence theorems and approximation rates.

Findings

Established pointwise and uniform convergence of the operators.

Derived rate of convergence using modulus of continuity.

Introduced a new approach to neural network approximation using Steklov integrals.

Abstract

The present paper deals with construction of newly family of Neural Network operators, that is, Steklov Neural Network operators. By using Steklov type integral, we introduce a new version of Neural Network operators and we obtain some convergence theorems for the family, such as, pointwise and uniform convergence, rate of convergence via modulus of continuity.