Estimates for Durrmeyer-type exponential sampling series in Mellin-Orlicz spaces

Kangal E., DİNLEMEZ KANTAR Ü.

Demonstratio Mathematica, vol.58, no.1, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1515/dema-2025-0155
  • Journal Name: Demonstratio Mathematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Keywords: logarithmic modulus of smoothness, Mellin-Lebesgue spaces, Mellin-Orlicz spaces, order of approximation
  • Gazi University Affiliated: Yes

Abstract

This study examines Durrmeyer-type exponential sampling series to obtain a quantitative estimate by using the concept of the logarithmic modulus of smoothness defined with the help of a suitable modular functional on Mellin-Orlicz spaces. Also, we want to underline that the spaces on which we study are reduced versions of Mellin-Orlicz spaces. Additionally, we obtain a further estimate for a particular case of Mellin-Lebesgue space, i.e., X 0 p, {X}_{0}^{p}, by utilizing an appropriate logarithmic modulus of smoothness that is different from the previous one. Also, we obtain direct estimates on the order of approximation for two different types of logarithmic Lipschitz classes by using previously mentioned results in involved sections.