Voronouskaya Univariate and Multivariate Asymptotic Expansions for Sigmoid Functions Induced Quasi-interpolation Neural Network Operators Revisited

Abstract

AbstractHere we study further the quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation functions relied 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. It follows [17].