Approximation by bivariate Bernstein-Kantorovich operators that reproduce exponential functions


Kanat K., Aksoy M., Altuntaş H.

Filomat, vol.39, no.10, pp.3489-3500, 2025 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 39 Issue: 10
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2510489k
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3489-3500
  • Keywords: Bernstein-Kantorovich operators, Bivariate operators, Modulus of continuity, Voronovskaya-type theorem
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

In this study, we construct bivariate Bernstein-Kantorovich polynomials which reproduce exponential function and investigate some approximation results for these operators. We use the test functions to prove Korovkin-type theorem. Then we obtain the rate of convergence by means of the modulus of continuity. We demonstrate the Voronovskaya-type theorem for the newly constructed operator. In the last section, we represent some illustrative graphics to show the convergence of the constructed operators and we give some numerical results.