On the Durrmeyer variant of q-Bernstein operators based on the shape parameter λ

Su L., Aslan R., Zheng F., Mursaleen M.

Journal of Inequalities and Applications, cilt.2023, sa.1, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2023 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1186/s13660-023-02965-7
  • Dergi Adı: Journal of Inequalities and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Durrmeyer operators, Lipschitz-type function, Peetre’s K-functional, q-Bernstein operators, Shape parameter λ
  • Van Yüzüncü Yıl Üniversitesi Adresli: Hayır

Özet

In this work, we consider several approximation properties of a Durrmeyer variant of q-Bernstein operators based on Bézier basis with the shape parameter λ∈ [− 1 , 1]. First, we calculate some moment estimates and show the uniform convergence of the proposed operators. Next, we investigate the degree of approximation with regard to the usual modulus of continuity, for elements of Lipschitz-type class and Peetre’s K-functional, respectively. Finally, to compare the convergence behavior and consistency of the related operators, we demonstrate some convergence and error graphs for certain λ∈ [− 1 , 1] and q-integers.