The errors of approximation for feedforward neural networks in the metric

Two classes of feedforward neural networks (FNNs) with one hidden layer are constructed to approximate L p integrable functions in this paper. We not only show that the constructed FNNs can approximate any f ∈ L p [ a , b ] ( 1 ≤ p < + ∞ ) arbitrarily in the L p metric as long as the number of hidden nodes is sufficiently large, but also reveal the relation among the approximation speed, the number of hidden nodes and the smoothness of the target function to be approximated by designing a novel method, which is originated from the Steklov mean function and the modulus of smoothness of f . The obtained results are helpful in studying the problem of approximation complexity of FNNs in the L p metric.