Direct and inverse approximation theorems of functions in the Orlicz type spaces SM

Chaichenko S., Shidlich A., ABDULLAYEV F.

Mathematica Slovaca, vol.69, no.6, pp.1367-1380, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.1515/ms-2017-0314
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1367-1380
  • Keywords: best approximation, direct theorem, inverse theorem, modulus of smoothness
  • Uşak University Affiliated: No

Abstract

In the Orlicz type spaces SM, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces SM.