Max-product neural network and quasi-interpolation operators activated by sigmoidal functions

The max-product neural network (NN) and quasi-interpolation (QI) operators are here introduced and studied. The density functions considered as kernels for the above operators are generated by certain finite linear combination of sigmoidal functions, and from them inherit very useful approximation properties. The convergence and the rate of approximation for the max-product NN and QI operators are studied. Estimates involving the modulus of continuity of the functions being approximated have been derived. Several examples are provided together with some applications and graphical representations. The relations with the general theory of neural networks and sampling operators are discussed in detail.