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Multiple general sigmoids based Banach space valued neural network multivariate approximation

dc.creatorAnastassiou, George A.
dc.date2023-12-22
dc.date.accessioned2024-04-16T14:16:57Z
dc.date.available2024-04-16T14:16:57Z
dc.identifierhttps://cubo.ufro.cl/ojs/index.php/cubo/article/view/3579
dc.identifier10.56754/0719-0646.2503.411
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/241510
dc.descriptionHere we present multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or \(\mathbb{R}^{N},\) \(N\in \mathbb{N}\), by the multivariate 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 modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by several different among themselves general sigmoid functions. This is done on the purpose to activate as many as possible neurons. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer. We finish with related \(L_{p}\) approximations.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttps://cubo.ufro.cl/ojs/index.php/cubo/article/view/3579/2328
dc.rightsCopyright (c) 2023 G. A. Anastassiouen-US
dc.rightshttps://creativecommons.org/licenses/by-nc/4.0/en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 25 No. 3 (2023); 411–439en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 25 No. 3 (2023); 411–439es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectGeneral sigmoid functionsen-US
dc.subjectmultivariate neural network approximationen-US
dc.subjectquasi-interpolation operatoren-US
dc.subjectKantorovich type operatoren-US
dc.subjectquadrature type operatoren-US
dc.subjectmultivariate modulus of continuityen-US
dc.subjectabstract approximationen-US
dc.subjectiterated approximationen-US
dc.subjectLp approximationen-US
dc.subject41A17en-US
dc.subject41A25en-US
dc.subject41A30en-US
dc.subject41A36en-US
dc.titleMultiple general sigmoids based Banach space valued neural network multivariate approximationen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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