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Here we study the multivariate quantitative symmetrized approximation of complex valued continuous functions on a box by complex valued symmetrized and perturbed multivariate neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the used function’s high order partial derivatives. The kind of our approximations are trigonometric and hyperbolic. Our multivariate symmetrized operators are defined by using a multivariate density function generated by a q-deformed and \(\lambda \) -parametrized hyperbolic tangent function. These enhanced approximations are pointwise and of the uniform norm. The related complex valued feed-forward neural networks are with one hidden layer.

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Multivariate Symmetrized and Perturbed Hyperbolic Tangent Based Complex Valued Trigonometric and Hyperbolic Neural Network Enhanced Approximation

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

Here we study the multivariate quantitative symmetrized approximation of complex valued continuous functions on a box by complex valued symmetrized and perturbed multivariate neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the used function’s high order partial derivatives. The kind of our approximations are trigonometric and hyperbolic. Our multivariate symmetrized operators are defined by using a multivariate density function generated by a q-deformed and \(\lambda \) -parametrized hyperbolic tangent function. These enhanced approximations are pointwise and of the uniform norm. The related complex valued feed-forward neural networks are with one hidden layer.