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- Publisher
- de Gruyter
- Copyright
- © 2023 George A. Anastassiou, published by Sciendo
- ISSN
- 1841-3307
- eISSN
- 1841-3307
- DOI
- 10.2478/awutm-2023-0005
- Publisher site
- See Article on Publisher Site
Abstract
AbstractHere we examine the multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝN , N ∈ 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 a hyperbolic tangent like sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.
Journal
Annals of West University of Timisoara - Mathematics – de Gruyter
Published: Jun 1, 2023
Keywords: Hyperbolic tangent like sigmoid function; multivariate neural network approximation; quasi-interpolation operator; Kantorovich type operator; quadrature type operator; multivariate modulus of continuity; abstract approximation; iterated approximation; 41A17; 41A25; 41A30; 41A36