Modified neural network operators and their convergence properties with summability methods

Abstract

We study the approximation properties of Cardaliaguet-Euvrard type neural network operators. We first modify the operators in order to get the uniform convergence, later we use regular summability matrix methods in the approximation by means of these operators to get more general results than the classical ones. We also display some examples and show graphical illustrations supporting our approximation results by neural networks operators. At the end of the paper we extend the theory to the multivariate case.