Approximation properties of a moment-based modification of Bernstein operators

GÜNGÖR Ş. Y.

AIMS Mathematics, cilt.10, sa.9, ss.21820-21834, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 9
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3934/math.2025970
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.21820-21834
  • Anahtar Kelimeler: Bernstein operators, modulus of continuity, rate of convergence, Voronovskaja-type theorem
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, a moment-based modification of the classical Bernstein operators is introduced. The proposed operators incorporate both a domain transformation and an adjustment by the second central moment to improve the approximation properties. We investigate their convergence behavior using tools such as the Lipschitz class and Peetre’s κ−functional. Quantitative estimates are established based on the classical and second-order modulus of continuity. Furthermore, a Voronovskaja-type theorem is provided to analyze the asymptotic behavior. Theoretical results are supported by numerical examples and graphical illustrations that demonstrate the effectiveness of the operators.