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Here we study the multivariate quantitaive approximation of multiple time separating random functions over a \(\mathbb {R}^{N},N\in \mathbb {N},\) by the normalized bell and squashing type multivariate neural network operators. Activation functions here are of compact support. These approximations are derived by establishing Jackson type multivariate inequalities involving the multivariate modulus of continuity of the engaged random function or its high order partial derivatives. The approximations are pointwise and with respect to the \(L_{P}\) norm. The feed-forward neural networks are with one hidden layer. We finish with a variety of interesting applications.

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Approximation of Multiple Time Separating Random Functions by Neural Networks Re Examined

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

Here we study the multivariate quantitaive approximation of multiple time separating random functions over a \(\mathbb {R}^{N},N\in \mathbb {N},\) by the normalized bell and squashing type multivariate neural network operators. Activation functions here are of compact support. These approximations are derived by establishing Jackson type multivariate inequalities involving the multivariate modulus of continuity of the engaged random function or its high order partial derivatives. The approximations are pointwise and with respect to the \(L_{P}\) norm. The feed-forward neural networks are with one hidden layer. We finish with a variety of interesting applications.