Approximation and Geometric Properties of Complex α -Bernstein Operator


Çetin N.

Results in Mathematics, cilt.74, sa.1, 2019 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 74 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s00025-018-0953-z
  • Dergi Adı: Results in Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Complex Bernstein operator, convexity, order of approximation, simultaneous approximation, spirallikeness, starlikeness, univalence, Voronovskaja type result, α-Bernstein operator
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Hayır

Özet

In this paper, we consider the complex form of a new generalization of the Bernstein operator, depending on a non-negative real parameter. We obtain quantitative upper estimate for simultaneous approximation, a qualitative Voronovskaja type result and the exact order of approximation. Also, we present some shape preserving properties of the complex α-Bernstein operator such as univalence, starlikeness, convexity and spirallikeness.