Quantitative approximation by multiple sigmoids Kantorovich-Shilkret quasi-interpolation neural network operators

Abstract

In this article, we derive multivariate quantitative approximation by Kantorovich-Shilkret type quasi-interpolation neural network operators with respect to supremum and $L_{p}$ norms. This is done with rates using the multivariate modulus of  continuity. We approximate continuous and bounded functions on $\mathbb{R}^{N},$ $N\in \mathbb{N}$. When they are also uniformly continuous, we have pointwise and uniform convergences, plus $L_{p}$ estimates. We include also the related Complex approximation. Our activation functions are induced by multiple general sigmoid functions.