Some Approximation Results by Bivariate Bernstein-Kantorovich Type Operators on a Triangular Domain

Aslan R., Izgi A.

Kyungpook Mathematical Journal, cilt.62, sa.3, ss.467-484, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 62 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.5666/kmj.2022.62.3.467
  • Dergi Adı: Kyungpook Mathematical Journal
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.467-484
  • Anahtar Kelimeler: Bernstein-kantorovich operators, Gbs type operators, Modulus of continuity, Peetre’s k-functional, Voronovskaya-type asymptotic theorem
  • Van Yüzüncü Yıl Üniversitesi Adresli: Hayır

Özet

In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre’s K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence