Approximation by the Extended Neural Network Operators of Kantorovich Type

Chenghao Xiang, Yi Zhao (), Xu Wang and Peixin Ye
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Chenghao Xiang: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Yi Zhao: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Xu Wang: Department of Mathematics and Statistics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada
Peixin Ye: School of Mathematics and LPMC, Nankai University, Tianjin 300071, China

Mathematics, 2023, vol. 11, issue 8, 1-17

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 L p [ − 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; L p space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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