Hyperbolic sigma-pi neural network operators for compactly supported continuous functions

It is the aim of this contribution to continue our investigations on a special family of hyperbolic-type linear operators (here, for compactly supported continuous functions on IRn) which immediately can be interpreted as concrete real-time realizations of three-layer feedforward neural networks with sigma-pi units in the hidden layer. To indicate how these results are connected with density results we start with some introductory theorems on this topic. Furthermore, we take a detailed look at the complexity of the generated neural networks in order to achieve global ε-accuracy.