Approximation by network operators with logistic activation functions

Abstract

This paper aims to study the construction and multivariate approximation of a class of network operators with logistic sigmoidal functions. First, a class of even and bell-shaped function with support on R is constructed by using appropriate translation and combination of the logistic function. Then, the constructed function is employed as activation function to construct a kind of so-called Cardaliaguet–Euvrard type network operators. Finally, these network operators are used to approximate bivariate functions in C[-1,1]2, and a Jackson type theorem for the approximation errors is established.