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In this chapter we study the multivariate smooth approximation under differentiation of functions. The approximators here are multivariate neural network operators activated by the symmetrized and perturbed hyperbolic tangent function. All the domains here are of \(\alpha \) whole Euclidean space. The multivariate neural network operators are of quasi-interpolation type: the basic ones, the Kantorovich type ones, and of the quadrature type. We give multivariate Voronovskaya type asymptotic expansions.

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Multivariate Voronovskaya Asymptotic Expansions for Symmetrized and Perturbed Hyperbolic Tangent 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 study the multivariate smooth approximation under differentiation of functions. The approximators here are multivariate neural network operators activated by the symmetrized and perturbed hyperbolic tangent function. All the domains here are of \(\alpha \) whole Euclidean space. The multivariate neural network operators are of quasi-interpolation type: the basic ones, the Kantorovich type ones, and of the quadrature type. We give multivariate Voronovskaya type asymptotic expansions.