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In this chapter we study the univariate quantitative smooth approximation, real and complex, ordinary and fractional under differentiation of functions. The approximators here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are of the whole real line. The neural network operators here are of quasi-interpolation type: the basic ones, the Kantorovich type ones, and of the quadrature type. We give pointwise and uniform approximations with rates. We finish with applications.

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Logistic Real and Complex, Ordinary and Fractional Neural Network Approximation Over Infinite Domains

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

In this chapter we study the univariate quantitative smooth approximation, real and complex, ordinary and fractional under differentiation of functions. The approximators here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are of the whole real line. The neural network operators here are of quasi-interpolation type: the basic ones, the Kantorovich type ones, and of the quadrature type. We give pointwise and uniform approximations with rates. We finish with applications.