J. Nonl. Evol. Equ. Appl. 2023 (6), pp. 87-103, published on October 12, 2023:

Abstract Voronovskaya type asymptotic expansions for general sigmoid functions based quasi-interpolation neural network operators

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis, TN 38152, U.S.A.

Received on April 17, 2023. Accepted on September 17, 2023.

Communicated by Gaston M. N'Guérékata

Abstract.  Here we reexamine further the quasi-interpolation general sigmoid function based neural network operators of one hidden layer. Based on fractional calculus theory we derive fractional Voronovskaya type asymptotic expansions for the approximation of these operators to the unit operator, as we are studying the univariate case. We treat also analogously the multivariate case by using Fréchet derivatives. The functions under approximation are Banach space valued.
Keywords: Neural Network Fractional Approximation, Multivariate Neural Network Approximation, Voronovskaya Asymptotic Expansions, fractional derivative, general sigmoid activation function.
2010 Mathematics Subject Classification:   26A33, 41A25, 41A45, 41A60.

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