Approximation by bivariate Bernstein–Kantorovich–Stancu operators that reproduce exponential functions

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Su L., Kanat K., Sofyalioğlu Aksoy M., Kisakol M.

Journal of Inequalities and Applications, cilt.2024, sa.1, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2024 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1186/s13660-024-03083-8
  • Dergi Adı: Journal of Inequalities and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Bernstein–Kantorovich–Stancu operators, Bivariate operators, Modulus of continuity, Voronovskaya-type theorem
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet

Özet

In this study, we construct a Stancu-type generalization of bivariate Bernstein–Kantorovich operators that reproduce exponential functions. Then, we investigate some approximation results for these operators. We use test functions to prove a Korovkin-type convergence theorem. Then, we show the rate of convergence by the modulus of continuity and give a Voronovskaya-type theorem. We give a covergence comparison about bivariate Bernstein–Kantorovich–Stancu operators and their exponential form.