Complex operators generated by q-Bernstein polynomials, q >= 1

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

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, vol.61, no.2, pp.169-176, 2016 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 2
  • Publication Date: 2016
  • Journal Name: STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.169-176
  • Keywords: q-Bernstein-type operator, Voronovskaja's theorem, quantitative estimates, complex rational operators, complex trigonometric polynomials
  • Ankara University Affiliated: Yes

Abstract

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