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

Su, Lian-Ta; Kangal, Esma; Kantar, ÜLKÜ; Cai, Qing-Bo

doi:10.3390/axioms13070485

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

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.