Approximation Properties of Some Modifications of Bernstein Operators

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Aslan R., Özger F.

Approximation Theory and Special Functions - ATSF 2024 Conference - 8th series, Ankara, Türkiye, 4 - 07 Eylül 2024, ss.77, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Ankara
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.77
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This presentation explores the approximation properties of the Stancu variant generalized Bernstein operators.

We analyze various moment estimates and investigate several local direct approximation theorems. Additionally,

we delve into further approximation features of these newly defined operators, including the Voronovskaya-type

asymptotic theorem and pointwise estimates. Through graphical and numerical comparisons with known linear

positive operators, we demonstrate superior approximation results in terms of convergence behavior, computa-

tional efficiency, and consistency. Finally, we apply these operators to obtain a numerical solution for a special

case of the fractional Volterra integral equation of the second kind.