Titlebook: Banach Space Valued Neural Network; Ordinary and Fractio George A. Anastassiou Book 2023 The Editor(s) (if applicable) and The Author(s), u

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General Multivariate Arctangent Function Induced Neural Network Approximations,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 approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate

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Quantitative Approximation by Kantorovich-Choquet Quasi-Interpolation Neural Network Operators Revitors with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on . .. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induc

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Quantitative Approximation by Kantorovich-Shilkret Quasi-interpolation Neural Network Operators Revo supremum norm. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on ., .. When they are additionally uniformly continuous we derive pointwise and uniform convergences. We include also the related Complex approximation. Our activat

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Voronouskaya Univariate and Multivariate Asymptotic Expansions for Sigmoid Functions Induced Quasi-rators of one hidden layer. Based on fractional calculus theory we derive fractional Voronovskaya type asymptotic expansions for the approximation of these operators to the unit operator, as we are studying the univariate case. We treat also analogously the multivariate case by using Fréchet derivat

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Multivariate Fuzzy Approximation by Neural Network Operators Induced by Several Sigmoid Functions Rc-Gudermannian-generalized symmetrical activation functions based neural network operators. These operators are multivariate fuzzy analogs of earlier studied multivariate Banach space valued ones. The derived results generalize earlier Banach space valued ones into the fuzzy level. Here the high ord

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Kommunales Rechtswesen/Rechtsämter 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