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Here we study further the symmetrized and perturbed hyperbolic tangent activated convolution type operators approximation properties. We derive Voronovskaya type asymptotic expansions for the errors of these approximations. We cover the cases of univariate: basic, Kantorovich and quadrature operators. We present ordinary and fractional results. At the end we give related simultaneous Voronovskaya type asymptotic expansions. Shape preservation via these operators is discussed too.

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Voronovskaya Asymptotic Expansions for the Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Convolution Operators, Ordinary and Fractional

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

Here we study further the symmetrized and perturbed hyperbolic tangent activated convolution type operators approximation properties. We derive Voronovskaya type asymptotic expansions for the errors of these approximations. We cover the cases of univariate: basic, Kantorovich and quadrature operators. We present ordinary and fractional results. At the end we give related simultaneous Voronovskaya type asymptotic expansions. Shape preservation via these operators is discussed too.