On a new construction of generalized q-bernstein polynomials based on shape parameter λ

Cai Q., Aslan R.

Symmetry, vol.13, no.10, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 10
  • Publication Date: 2021
  • Doi Number: 10.3390/sym13101919
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: (λ, q)-Bernstein polynomials, Lipschitz-type class, Order of convergence, Q-calculus, Shape parameter λ
  • Van Yüzüncü Yıl University Affiliated: No


This paper deals with several approximation properties for a new class of q-Bernstein polynomials based on new Bernstein basis functions with shape parameter λ on the symmetric interval [−1, 1]. Firstly, we computed some moments and central moments. Then, we constructed a Korovkin-type convergence theorem, bounding the error in terms of the ordinary modulus of smoothness, providing estimates for Lipschitz-type functions. Finally, with the aid of Maple software, we present the comparison of the convergence of these newly constructed polynomials to the certain functions with some graphical illustrations and error estimation tables.