Complex operators generated by q-Bernstein polynomials, q ≥ 1


BAŞCANBAZ TUNCA G., ÇETİN N., Gal S. G.

Studia Universitatis Babes-Bolyai Mathematica, cilt.61, sa.2, ss.169-176, 2016 (Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 2
  • Basım Tarihi: 2016
  • Dergi Adı: Studia Universitatis Babes-Bolyai Mathematica
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.169-176
  • Anahtar Kelimeler: Complex rational operators, Complex trigonometric polynomials, Q-Bernstein-type operator, Quantitative estimates, Voronovskaja's theorem
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet

Özet

By using a univalent and analytic function τ in a suitable open disk centered in origin, we attach to analytic functions f, the complex Bernsteintype operators of the form Bn,q τ (f) = Bn,q (f ο τ-1) ο τ, where Bn,q denote the classical complex q-Bernstein polynomials, q ≥ 1. The new complex operators satisfy the same quantitative estimates as Bn,q. As applications, for two concrete choices of τ, we construct complex rational functions and complex trigonometric polynomials which approximate f with a geometric rate.