On the Properties of the Modified <i>λ</i>-Bernstein-Stancu Operators

Lin Z., Torun G., Kangal E., DİNLEMEZ KANTAR Ü., Cai Q.

SYMMETRY-BASEL, cilt.16, sa.10, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 10
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/sym16101276
  • Dergi Adı: SYMMETRY-BASEL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Gazi Üniversitesi Adresli: Evet

Özet

In this study, a new kind of modified lambda-Bernstein-Stancu operators is constructed. Compared with the original lambda-B & eacute;zier basis function, the newly operator basis function is more concise in form and has certain symmetry beauty. The moments and central moments are computed. A Korovkin-type approximation theorem is presented, and the degree of convergence is estimated with respect to the modulus of continuity, Peetre's K-functional, and functions of the Lipschitz-type class. Moreover, the Voronovskaja type approximation theorem is examined. Finally, some numerical examples and graphics to show convergence are presented.