Some Statistical and Direct Approximation Properties for a New Form of the Generalization of q-Bernstein Operators with the Parameter λ

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Su L., Kangal E., Kantar Ü., Cai Q.

AXIOMS, cilt.13, sa.7, 2024 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 7
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/axioms13070485
  • Dergi Adı: AXIOMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Gazi Üniversitesi Adresli: Evet

Özet

In this study, a different generalization of q-Bernstein operators with the parameter lambda is an element of [-1,1] is created. The moments and central moments of these operators are calculated, a statistical approximation result for this new type of (lambda,q)-Bernstein operators is obtained, and the convergence properties are analyzed using the Peetre K-functional and the modulus of continuity for this new operator. Finally, a numerical example is given to illustrate the convergence behavior of the newly defined operators.