Asymptotic expansions and Voronovskaja type theorems for the multivariate neural network operators

Abstract

In this paper, an asymptotic formula for the so-called multivariate neural network (NN) operators has been established. As a direct consequence, a first and a second order pointwise Voronovskaja type theorem has been reached. At the end, the particular case of the NN operators activated by the logistic function has been treated in details.