On function approximators implementable as layered neural networks

The paper deals with the approximation of continuous functions by feedforward neural networks. In the first part of paper are presented some main results of Y. Ito (1992) and P. Cardaliaguet and G. Euvrard (1992) regarding universal approximators implementable as four-layer neural networks. In the second part is presented an explicit formula similar to Cybenko expression for approximating a continuous multivariate function using characteristic function as a particular bell-shaped function in place of sigmoidal function. This approximation formula is implementable as three-layer feedforward neural networks that, surprisingly, have in the hidden layer the same number of neurons as Ito and Cardaliaguet-Euvrard four-layer neural networks have in the second hidden layer