Symmetrized, Perturbed Hyperbolic Tangent-Based Complex-Valued Trigonometric and Hyperbolic Neural Network Accelerated Approximation
In this study, 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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/10/1688 |
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| Summary: | In this study, 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 kinds of our approximations are trigonometric and hyperbolic. Our symmetrized operators are defined by using a density function generated by a <i>q</i>-deformed and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-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 have one hidden layer. |
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| ISSN: | 2227-7390 |