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Keywords = trigonometric- and hyperbolic-type Taylor formulae

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27 pages, 957 KiB  
Article
Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function
by Seda Karateke
Mathematics 2025, 13(3), 453; https://doi.org/10.3390/math13030453 - 29 Jan 2025
Viewed by 765
Abstract
This paper deals with a family of normalized multivariate neural network (MNN) operators of complex-valued continuous functions for a multivariate context on a box of RN¯, N¯N. Moreover, we consider the case of approximation employing iterated [...] Read more.
This paper deals with a family of normalized multivariate neural network (MNN) operators of complex-valued continuous functions for a multivariate context on a box of RN¯, N¯N. Moreover, we consider the case of approximation employing iterated MNN operators. In addition, pointwise and uniform convergence results are obtained in Banach spaces thanks to the multivariate versions of trigonometric and hyperbolic-type Taylor formulae on the corresponding feed-forward neural networks (FNNs) based on one or more hidden layers. Full article
(This article belongs to the Special Issue Approximation Theory and Applications)
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27 pages, 326 KiB  
Article
Parametrized Half-Hyperbolic Tangent Function-Activated Complex-Valued Neural Network Approximation
by George A. Anastassiou and Seda Karateke
Symmetry 2024, 16(12), 1568; https://doi.org/10.3390/sym16121568 - 23 Nov 2024
Cited by 1 | Viewed by 812
Abstract
In this paper, we create a family of neural network (NN) operators employing a parametrized and deformed half-hyperbolic tangent function as an activation function and a density function produced by the same activation function. Moreover, we consider the univariate quantitative approximations by complex-valued [...] Read more.
In this paper, we create a family of neural network (NN) operators employing a parametrized and deformed half-hyperbolic tangent function as an activation function and a density function produced by the same activation function. Moreover, we consider the univariate quantitative approximations by complex-valued neural network (NN) operators of complex-valued functions on a compact domain. Pointwise and uniform convergence results on Banach spaces are acquired through trigonometric, hyperbolic, and hybrid-type hyperbolic–trigonometric approaches. Full article
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