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, vol.130, no.3, pp.1479-1493, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 130 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.32604/cmes.2022.018338
  • Journal Name: CMES - Computer Modeling in Engineering and Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1479-1493
  • Keywords: (λ,q)-Bernstein polynomials, Lipschitz-type function, Order of convergence, Peetre's K-functional, Q-calculus
  • Van Yüzüncü Yıl University Affiliated: No

Abstract

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.