Multivariate symmetrized, \(q\)-deformed and \(\lambda\)-parametrized hyperbolic tangent induced complex valued trigonometric and hyperbolic neural network enhanced approximation

George A. Anastassiou

doi:10.56754/0719-0646.2802.323

DOI:

https://doi.org/10.56754/0719-0646.2802.323

Abstract

Here we study the multivariate quantitative symmetrized approximation of complex valued continuous functions on a box by complex valued symmetrized and perturbed multivariate neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the used function's high order partial derivatives. The kind of our approximations are trigonometric and hyperbolic. Our multivariate symmetrized operators are defined by using a multivariate density function generated by a \(q\)-deformed and \(\lambda\)-parametrized hyperbolic tangent function. These enhanced approximations are pointwise and of the uniform norm. The related complex valued feed-forward neural networks are with one hidden layer.

Keywords

q-deformed and λ-parametrized hyperbolic tangent , complex valued symmetrized multivariate neural network approximation , complex valued multivariate quasi-interpolation operator , modulus of continuity , trigonometric and hyperbolic enhanced approximation

Mathematics Subject Classification:

41A17 , 41A25 , 41A99 , 42A10

George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A. https://orcid.org/0000-0002-3781-9824

Pages: 323-347
Date Published: 2026-05-18
Vol. 28 No. 2 (2026)

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