A new kind of Durrmeyer-Stancu-type operators

Cai Q., GÜNGÖR Ş. Y., ÇEKİM B.

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-2025-0132
  • Journal Name: DEMONSTRATIO MATHEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Gazi University Affiliated: Yes

Abstract

The objective of this study is to examine a class of positive linear operators, defined in terms of the b psi , k lambda , mu {b}_{\psi ,k}<^>{\lambda ,\mu } basis and to analyze their approximation properties. Direct estimates for the ( lambda , mu ) \left(\lambda ,\mu ) -Durrmeyer-Stancu-type operators are obtained using the first modulus of continuity and in a certain Lipschitz-type space. Approximation properties of these operators in Lebesgue spaces are also given. Finally, illustrative graphics are provided to support the results and to compare the rate of convergence.