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In this chapter we research the univariate smooth approximation ordinary and fractional under differentiation of functions. The approximators here are neural network operators activated by the symmetrized and perturbed hyperbolic tangent function. All domains here 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 Voronovskaya type asymptotic expansions.

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Voronovskaya Asymptotic Expansions for Symmetrized and Perturbed Hyperbolic Tangent Ordinary and Fractional Neural Network Approximations 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 research the univariate smooth approximation ordinary and fractional under differentiation of functions. The approximators here are neural network operators activated by the symmetrized and perturbed hyperbolic tangent function. All domains here 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 Voronovskaya type asymptotic expansions.