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By using a univalent and analytic function τ in a suitable open diskcentered in origin, we attach to analytic functions f, the complex Bernstein type operators of the form Bτ n,q(f) = Bn,q (f ο τ-1),οτ where Bn,q denote the classical complex q-Bernstein polynomials, q ³ 1. The new complex operators satisfy the same quantitative estimates as Bn,q . As applications, for two concretechoices of τ , we construct complex rational functions and complex trigonometric polynomials which approximate f with a geometric rate.
Mathematics Subject Classification (2010):
Keywords: q-Bernstein-type operator, Voronovskajas theorem, quantitative estimates, complex rational operators, complex trigonometric polynomials
