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中文摘要：
研究一类近似插值单隐层前向神经网络的逼近问题。利用Steklov平均函数,以光滑模为度量,估计了该网络对Lebesgue可积函数的逼近误差。所获结果表明：对于定义在[a,b]上的任意p（1≤p〈＋∞）次Lebesgue可积函数f（x）,只要隐层节点数n足够大,均有一个近似插值神经网络以任意精度逼近f（x）。
英文摘要：
For a class of approximation interpolation feedforward neural networks （ai-nets） with single hidden layer, the problem of approximation is studied in this paper. With the Steklov mean func- tion, the errors for the interpolation neural networks approximating Lebesgue integrable functions are estimated by the modulus of smoothness. It is shown that for a ai-net can approximate, with arbitrary precision, anyp-th （1 ≤p〈＋∞） Lebesgue integrable functionf（x） defined on [a, b] as long as the num- ber of hidden nodes n is sufficiently large.
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