Complex Operators Generated by q-Bernstein Polynomials, q≥1: Dedicated to the memory of Akif D. Gadjiev - BAȘCANBAZ-TUNCA, Gülen; ÇETIN, Nursel; GAL, Sorin G. (Studia Universitatis Babeș-Bolyai Mathematica, 2016)
By using an univalent and analytic function τ in a suitable open disk centered in origin, we attach to analytic functions f, the complex Bernstein-type operators of the form B_{n,q}^{τ}(f)=B_{n,q}(f∘τ⁻¹)∘τ , where B_{n,q} denote the classical complex q-Bernstein polynomials, q≥1. The new complex operators satisfy the same quantitative estimates as B_{n,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. Mathematics Subject Classification (2010): 30E10, 41A35, 41A25.