Approximation properties of univariate and bivariate new class λ -Bernstein–Kantorovich operators and its associated GBS operators

Aslan R.

Computational and Applied Mathematics, vol.42, no.1, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1007/s40314-022-02182-w
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: GBS type operators, Lipschitz-type class, Mixed modulus of continuity, Peetre’s K-functional, λ-Bernstein operators
  • Van Yüzüncü Yıl University Affiliated: No


The main objective of this work is to derive some approximation properties of univariate and bivariate Kantorovich type new class Bernstein operators by means of shape parameter λ∈ [- 1 , 1]. We obtained some basic results such as moments estimates and Korovkin type approximation theorem. Next, we estimated the degree of convergence in terms of the usual modulus of continuity, for an element of Lipschitz type continuous functions and Peetre’s K-functional, respectively. Moreover, we constructed the bivariate of newly introduced operators and computed the rate of approximation in connection with the partial and complete modulus of continuity, also for the elements of the Lipschitz type class. In addition, we proposed the associated Generalized Boolean Sum (GBS) type of bivariate operators and calculated the order of approximation with the help of mixed modulus of continuity and a class of the Lipschitz of Bögel type continuous functions. Finally, we presented some graphics and an error of estimation table to compare the convergence behavior of univariate, bivariate forms and its associated GBS type operators to certain functions.