Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>&l...
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MDPI AG
2025-01-01
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| author | Seda Karateke |
| author_facet | Seda Karateke |
| author_sort | Seda Karateke |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mover><mi>N</mi><mo>¯</mo></mover></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi>N</mi><mo>¯</mo></mover><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></semantics></math></inline-formula>. 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. |
| format | Article |
| id | doaj-art-ad3e9cda16e2459b9ff84bbe4a449394 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-ad3e9cda16e2459b9ff84bbe4a4493942025-08-20T02:12:25ZengMDPI AGMathematics2227-73902025-01-0113345310.3390/math13030453Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent FunctionSeda Karateke0Department of Software Engineering, Faculty of Engineering and Natural Sciences, Istanbul Atlas University, 34408 Istanbul, TürkiyeThis 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mover><mi>N</mi><mo>¯</mo></mover></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi>N</mi><mo>¯</mo></mover><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></semantics></math></inline-formula>. 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.https://www.mdpi.com/2227-7390/13/3/453multi-layer approximationparameterized half-hyperbolic tangent functionmultivariate trigonometric and hyperbolic neural network approximationmultivariate modulus of continuityiterated approximationmultivariate density function |
| spellingShingle | Seda Karateke Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function Mathematics multi-layer approximation parameterized half-hyperbolic tangent function multivariate trigonometric and hyperbolic neural network approximation multivariate modulus of continuity iterated approximation multivariate density function |
| title | Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function |
| title_full | Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function |
| title_fullStr | Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function |
| title_full_unstemmed | Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function |
| title_short | Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function |
| title_sort | complex valued multivariate neural network mnn approximation by parameterized half hyperbolic tangent function |
| topic | multi-layer approximation parameterized half-hyperbolic tangent function multivariate trigonometric and hyperbolic neural network approximation multivariate modulus of continuity iterated approximation multivariate density function |
| url | https://www.mdpi.com/2227-7390/13/3/453 |
| work_keys_str_mv | AT sedakarateke complexvaluedmultivariateneuralnetworkmnnapproximationbyparameterizedhalfhyperbolictangentfunction |