Some approximation results for the new modification of bernstein-beta operators

Cai Q., Sofyalıoğlu M., Kanat K., ÇEKİM B.

AIMS Mathematics, cilt.7, sa.2, ss.1831-1844, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3934/math.2022105
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1831-1844
  • Anahtar Kelimeler: Korovkin type approximation theorem, modulus of continuity, functions of Lipschitz class, Peetre's K-functionals
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet

Özet

This paper deals with the newly modification of Beta-type Bernstein operators, preserving constant and Korovkin’s other test functions ei = ti, i = 1, 2 in limit case. Then the uniform convergence of the constructed operators is given. The rate of convergence is obtained in terms of modulus of continuity, Peetre-K functionals and Lipschitz class functions. After that, the Voronovskaya-type asymptotic result for these operators is established. At last, the graphical results of the newly defined operators are discussed.