Quantitative approximation by perturbed Kantorovich–Choquet neural network operators
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This paper deals with the determination of the rate of convergence to the unit of perturbed Kantorovich–Choquet univariate and multivariate normalized neural network operators of one hidden layer. These are given through the univariate and multivariate moduli of continuity of the involved univariate or multivariate function or its high order derivatives and that appears in the right-hand side of the associated univariate and multivariate Jackson type inequalities. The activation function is very general, especially it can derive from any univariate or multivariate sigmoid or bell-shaped function. The right hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of Kantorovich–Choquet type. We give applications for the first derivatives of the involved function.
KeywordsUnivariate and multivariate neural network approximation Univariate and multivariate perturbation of operators Modulus of continuity Jackson type inequality Choquet integral
Mathematics Subject Classification41A17 41A25 41A30 41A35