Geodesic
Quantitative approximation by multiple sigmoids Kantorovich-Shilkret quasi-interpolation neural network operators
George A. Anastassiou1 ; George A. Anastassiou
1Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
Acta mathematica Universitatis Comenianae, Tome 92 (2023) no. 3, pp. 241-251 
George A. Anastassiou; George A. Anastassiou. Quantitative approximation by multiple sigmoids Kantorovich-Shilkret quasi-interpolation neural network operators. Acta mathematica Universitatis Comenianae, Tome 92 (2023) no. 3, pp. 241-251. http://geodesic.mathdoc.fr/item/AMUC_2023_92_3_a3/
@article{AMUC_2023_92_3_a3,
     author = {George A. Anastassiou and George A. Anastassiou},
     title = { Quantitative approximation by multiple sigmoids {Kantorovich-Shilkret} quasi-interpolation neural network operators},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {241--251},
     year = {2023},
     volume = {92},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2023_92_3_a3/}
}
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In this article, we derive multivariate quantitative approximation by Kantorovich-Shilkret type quasi-interpolation neural network operators with respect to supremum and $L_{p}$ norms. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on $\mathbb{R}^{N},$ $N\in \mathbb{N}$. When they are also uniformly continuous, we have pointwise and uniform convergences, plus $L_{p}$ estimates. We include also the related Complex approximation. Our activation functions are induced by multiple general sigmoid functions.