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Approximation by the Extended Neural Network Operators of Kantorovich Type

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chenghao Xiang & Yi Zhao & Xu Wang & Peixin Ye, 2023. "Approximation by the Extended Neural Network Operators of Kantorovich Type," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1903-:d:1125803
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