Direct and inverse approximation theorems in the weighted orlicz-type spaces with a variable exponent

ABDULLAYEV F., Chaichenko S., Kyzy M. I., Shidlich A.

Turkish Journal of Mathematics, cilt.44, sa.1, ss.284-299, 2020 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3906/mat-1911-3
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.284-299
  • Anahtar Kelimeler: Best approximation, Direct approximation theorem, Inverse approximation theorem, K-functionals, Modulus of smoothness, Orlicz-type spaces, Weighted space
  • Uşak Üniversitesi Adresli: Hayır

Özet

In weighted Orlicz-type spaces Sp, μ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre K-functionals is shown in the spaces Sp, μ.