Smooth Logistic Real and Complex, Ordinary and Fractional Neural Network Approximations over Infinite Domains

In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are obtained from the whole real line. The neural network operators used here are of the quasi-interpolation type: basic ones, Kantorovich-type ones, and those of the quadrature type. We provide pointwise and uniform approximations with rates. We finish with their applications.