Interpolation for neural-network operators activated with a generalized logistic-type function

Uyan H., Aslan A. O., Karateke S., BÜYÜKYAZICI İ.

Journal of Inequalities and Applications, cilt.2024, sa.1, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2024 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1186/s13660-024-03199-x
  • Dergi Adı: Journal of Inequalities and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Generalized logistic-type function, Interpolation, Neural-Network (NN) operators, Order of approximation, Uniform approximation
  • Ankara Üniversitesi Adresli: Evet

Özet

This paper defines a family of neural-network interpolation operators. The first derivative of generalized logistic-type functions is considered as a density function. Using the first-order uniform approximation theorem for continuous functions defined on the finite intervals, the interpolation properties of these operators are presented. A Kantorovich-type variant of the operators Fna,ε is also introduced. The approximation of Kantorovich-type operators in LP spaces with 1≤p≤∞ is studied. Further, different combinations of the parameters of our generalized logistic-type activation function θs,a are examined to see which parameter values might give us a more efficient activation function. By choosing suitable parameters for the operator Fna,ε and the Kantorovich variant of the operator Fna,ε, the approximation of various function examples is studied.