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Here we research the univariate quantitative symmetrized approximation of complex valued continuous functions on a compact interval by complex valued symmetrized and perturbed neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the used function’s high order derivatives. The kind of our approximations are trigonometric and hyperbolic. Our symmetrized operators are defined by using a density function generated by a q-deformed and \(\lambda \) -parametrized hyperbolic tangent function, which is a sigmoid function. These accelerated 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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Symmetrized and Perturbed Hyperbolic Tangent Relied Complex Valued Trigonometric and Hyperbolic Neural Network Accelerated Approximation

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

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