Approximation by Exponential Type Neural Network Operators

TL;DR

This paper introduces a new family of exponential type neural network operators using sigmoidal functions, establishing their approximation properties and extending them to multivariate cases.

Contribution

The paper presents a novel class of exponential type neural network operators with theoretical approximation results and multivariate extensions, advancing neural network approximation theory.

Findings

Established point-wise and uniform approximation theorems.

Provided quantitative estimates of approximation order.

Extended operators to multivariate functions.

Abstract

In the present article, we introduce and study the behaviour of the new family of exponential type neural network operators activated by the sigmoidal functions. We establish the point-wise and uniform approximation theorems for these NN (Neural Network) operators in C[a; b]: Further, the quantitative estimates of order of approximation for the proposed NN operators in C(N)[a; b] are established in terms of the modulus of continuity. We also analyze the behaviour of the family of exponential type quasi-interpolation operators in C(R+): Finally, we discuss the multivariate extension of these NN operators and some examples of the sigmoidal functions.