Modular Convergence of Semi-discrete Neural Network Operators in Orlicz space

Priyanka Majethiya

Session: General

Keywords: Function approximation, Neural networks operators, Orlicz space, Sigmoidal Function

Abstract:

Neural network (NN) operators are widely recognized for providing a constructive approach to approximate given class of functions.
In this paper, we study the convergence of a family of semi-discrete NN operators, known as \textit{Durrmeyer} type NN operators, in the general framework of \textit{Orlicz spaces} on $[a,b] (\subset \mathbb{R}),$ denoted by $L^{\phi}([a,b]).$ The Orlicz space consists of various function spaces, including classical \textit{Lebesgue spaces, Exponential spaces, Zygmund spaces}, for different choices of $\phi-$functions. Hence this note presents a unified approximation procedure for these operators across various function spaces. We establish the boundedness of Durrmeyer type NN operators within $L^{\phi}([a,b]).$ Further, modular convergence theorem is deduced for these NN operators in general setting of Orlicz spaces. Lastly, we enclose some graphical representations and error-estimates to demonstrate the approximation process.

Submission Number: 83