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

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.