q-Deformed and λ-Parametrized Hyperbolic Tangent Function Relied Complex Valued Trigonometric and Hyperbolic Neural Network High Order Approximations
George A. Anastassiou · 2024
The author researches the univariate quantitative approximation of complex-valued continuous functions on a compact interval by complex-valued neural network operators. These approximations are derived by establishing Jackson-type inequalities involving the modulus of continuity of the engaged function’s high-order derivatives. The nature of the author’s approximations is trigonometric and hyperbolic. His operators are defined by using a density function generated by a q-deformed and l-parametrized hyperbolic tangent function, which is a sigmoid function. The approximations are pointwise and of the uniform norm. The related complex valued feed-forward neural networks are with one hidden layer.