Convergence Analysis of Max-Min Exponential Neural Network Operators in Orlicz Space

TL;DR

This paper introduces a Max Min exponential neural network operator framework, extending it to Kantorovich-type operators, analyzing their convergence in various spaces, and illustrating their approximation capabilities with graphical examples.

Contribution

It develops and analyzes Max Min Kantorovich exponential neural network operators, extending approximation theory within Orlicz spaces and providing convergence rate estimates.

Findings

Established pointwise and uniform convergence for univariate functions.

Derived convergence rates using logarithmic modulus of continuity.

Demonstrated approximation error through graphical illustrations.

Abstract

In this current work, we propose a Max Min approach for approximating functions using exponential neural network operators. We extend this framework to develop the Max Min Kantorovich-type exponential neural network operators and investigate their approximation properties. We study both pointwise and uniform convergence for univariate functions. To analyze the order of convergence, we use the logarithmic modulus of continuity and estimate the corresponding rate of convergence. Furthermore, we examine the convergence behavior of the Max Min Kantorovich type exponential neural network operators within the Orlicz space setting. We provide some graphical representations to illustrate the approximation error of the function through suitable kernel and sigmoidal activation functions.