Multivariate Approximation With Rates by Perturbed Kantorovich-Shilkret Neural Network Operators

Abstract

This paper deals with the determination of the rate of convergence to the unit of Perturbed Kantorovich-Shilkret multivariate normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the engaged multivariate function or its high order partial derivatives and that appears in the associated multivariate Jackson type inequalities. The activation function is very general and it can derive from any multivariate sigmoid or bell-shaped functions. The right hand sides of our Jackson type inequalities do not depend on the activation function. The sample functionals are Kantorovich-Shilkret type. We provide an application for the first partial derivatives of the involved function.