Approximation by the Extended Neural Network Operators of Kantorovich Type

Abstract

Based on the idea of integral averaging and function extension, an extended Kantorovich-type neural network operator is constructed, and its error estimate of approximating continuous functions is obtained by using the modulus of continuity. Furthermore, by introducing the normalization factor, the approximation property of the new version of the extended Kantorovich-type neural network (normalized extended Kantorovich-type neural network) operator is obtained in Lp[−1,1]. The numerical examples show that this newly proposed neural network operator has a better approximation performance than the classical one, especially at the endpoints of a compact interval.

Keywords

• neural networks
• Kantorovich-type operator
• approximation
• modulus of continuity
• <i>L_p</i> space