Titlebook: Parametrized, Deformed and General Neural Networks; George A. Anastassiou Book 2023 The Editor(s) (if applicable) and The Author(s), under

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Banach Space Valued Ordinary and Fractional Neural Networks Approximations Based on the Parametrized Gudermannian Function,or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative or fractional derivatives.

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Banach Space Valued Univariate Neural Network Approximation Based on Parametrized Error Activation Function,uasi-interpolation Banach space valued neural network operators. We perform also the related Banach space valued fractional approximation. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued

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Banach Space Valued Multivariate Multi Layer Neural Network Approximation Based on Parametrized Error Activation Function,e normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types, these correspond to hidden multi-layer neural networks. The approximations are derived by establishing multidimensio

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