Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ

Cai Q., Aslan R.

CMES - Computer Modeling in Engineering and Sciences, cilt.130, sa.3, ss.1479-1493, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 130 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.32604/cmes.2022.018338
  • Dergi Adı: CMES - Computer Modeling in Engineering and Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1479-1493
  • Anahtar Kelimeler: (λ,q)-Bernstein polynomials, Lipschitz-type function, Order of convergence, Peetre's K-functional, Q-calculus
  • Van Yüzüncü Yıl Üniversitesi Adresli: Hayır

Özet

The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to Bézier basis functions with shape parameter λ ∈ [−1, 1]. Firstly, we compute some basic results such as moments and central moments, and derive the Korovkin type approximation theorem for these operators. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz-type class and Peetre's K-functional, respectively. Lastly, with the aid of Maple software, we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.