Symmetrized, Perturbed Hyperbolic Tangent-Based Complex-Valued Trigonometric and Hyperbolic Neural Network Accelerated Approximation

George A. Anastassiou ()
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George A. Anastassiou: Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

Mathematics, 2025, vol. 13, issue 10, 1-11

Abstract: In this study, we research the univariate quantitative symmetrized approximation of complex-valued continuous functions on a compact interval by complex-valued symmetrized and perturbed neural network operators. These approximations are derived by establishing Jackson-type inequalities involving the modulus of continuity of the used function’s high order derivatives. The kinds of our approximations are trigonometric and hyperbolic. Our symmetrized operators are defined by using a density function generated by a q -deformed and λ -parametrized hyperbolic tangent function, which is a sigmoid function. These accelerated approximations are pointwise and of the uniform norm. The related complex-valued feed-forward neural networks have one hidden layer.

Keywords: q -deformed and λ -parametrized hyperbolic tangent; complex-valued symmetrized neural network approximation; complex-valued quasi-interpolation operator; modulus of continuity; trigonometric and hyperbolic accelerated approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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