Richards’s curve induced Banach space valued multivariate neural network approximation

  • Yazar SEDA KARATEKE
  • Yayın Türü Makale
  • Yayın Yılı 2022
  • DOI 10.1007/s40065-022-00414-9
  • Yayıncı Springer
  • Dergi Arabian Journal of Mathematics
  • Tek Biçim Adres https://hdl.handle.net/20.500.14081/1777

Here, we present multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or RN , N ∈ N, by the multivariate normalized, quasi-interpolation, Kantorovichtype and quadrature-type neural network operators. We examine also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high-order Fréchet derivatives. Our multivariate operators are defined using a multidimensional density function induced by the Richards’s curve, which is a generalized logistic function. The approximations are pointwise, uniform and L p. The related feed-forward neural network is with one hidden layer.

Görüntülenme
61
24.02.2023 tarihinden bu yana
İndirme
1
24.02.2023 tarihinden bu yana
Son Erişim Tarihi
10 Kasım 2023 10:39
Google Kontrol
Tıklayınız
multivariate function approximations operators neural network multidimensional derivatives Fréchet defined high-order density induced Richards’s engaged modulus generalized logistic pointwise uniform related feed-forward hidden continuity involving quasi-interpolation present quantitative Banach valued continuous functions normalized Kantorovichtype inequalities
Tam Metin
Detaylı Görünüm
Eser AdıRichards’s curve induced Banach space valued multivariate neural network approximation
YazarSEDA KARATEKE
Yayın Yılı2022
Yayın TürüMakale
ÖzetHere, we present multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or RN , N ∈ N, by the multivariate normalized, quasi-interpolation, Kantorovichtype and quadrature-type neural network operators. We examine also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high-order Fréchet derivatives. Our multivariate operators are defined using a multidimensional density function induced by the Richards’s curve, which is a generalized logistic function. The approximations are pointwise, uniform and L p. The related feed-forward neural network is with one hidden layer.
Açık Erişim Tarihi2022-11-13
YayıncıSpringer
DilENGLISH
Konu Başlıkları41A17
Konu Başlıkları 41A25
Konu Başlıkları41A30
Konu Başlıkları41A36
Tek Biçim Adreshttps://hdl.handle.net/20.500.14081/1777
DergiArabian Journal of Mathematics
DOI10.1007/s40065-022-00414-9
Orcid0000-0003-1219-0115
Analizler
Yayın Görüntülenme
Yayın Görüntülenme
Erişilen ülkeler
Erişilen şehirler
6698 sayılı Kişisel Verilerin Korunması Kanunu kapsamında yükümlülüklerimiz ve çerez politikamız hakkında bilgi sahibi olmak için alttaki bağlantıyı kullanabilirsiniz.
Tamam
creativecommons
Bu site altında yer alan tüm kaynaklar Creative Commons Alıntı-GayriTicari-Türetilemez 4.0 Uluslararası Lisansı ile lisanslanmıştır.
Platforms