A survey on approximation by means of neural network operators

Abstract

In the present survey, we recall the main convergence results concerning the theory of neural network (NN) operators. Pointwise and uniform approximation results have been proved for the classical (linear) NN operators, as well as, for their corresponding max-product (nonlinear) version, when continuous functions dened on bounded domains are approximated. In order to approximate also not necessarily continuous functions, a Kantorovich-type version of the above NN operators has been studied in an Lp-setting. Finally, several examples of sigmoidal activation functions for the aforementioned operators have been provided.