Approximation by bivariate Bernstein-Kantorovich operators that reproduce exponential functions


Kanat K., Aksoy M., Altuntaş H.

Filomat, cilt.39, sa.10, ss.3489-3500, 2025 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 10
  • Basım Tarihi: 2025
  • Doi Numarası: 10.2298/fil2510489k
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3489-3500
  • Anahtar Kelimeler: Bernstein-Kantorovich operators, Bivariate operators, Modulus of continuity, Voronovskaya-type theorem
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet

Özet

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.