Jackson-type inequalities and widths of functional classes in the Musielak–Orlicz type spaces

ABDULLAYEV F., Chaichenko S., Imashkyzy M., Shidlich A.

Rocky Mountain Journal of Mathematics, cilt.51, sa.4, ss.1143-1155, 2021 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1216/rmj.2021.51.1143
  • Dergi Adı: Rocky Mountain Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.1143-1155
  • Anahtar Kelimeler: Bernstein width, Best approximation, Jackson-type inequality, Kolmogorov width, Module of smoothness, Musielak–Orlicz spaces
  • Uşak Üniversitesi Adresli: Hayır

Özet

In the Musielak–Orlicz-type spaces SM, exact Jackson-type inequalities are obtained in terms of best approximations of functions and the averaged values of their generalized moduli of smoothness. The values of Kolmogorov, Bernstein, linear, and projective widths in SM are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.