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, vol.44, no.1, pp.284-299, 2020 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1911-3
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.284-299
  • Keywords: Best approximation, Direct approximation theorem, Inverse approximation theorem, K-functionals, Modulus of smoothness, Orlicz-type spaces, Weighted space
  • Uşak University Affiliated: No

Abstract

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.