On the convergence of bieberbach polynomials in domains with interior zero angles

Abstract

Let G⊂C be a finite Jordan domain, 0εG and w = φ(z) be the conformal mapping of G onto a disc normalized by . It is well known that the uniform convergence of Bieberbach polynomials for the pair (G, 0) to φ(z) in Ǥ is governed by the properties of ∂G. In this study, the decrease of to zero and the estimation of this error in domains with interior zero angles are determined depending on the properties of boundary arcs and the degree of their touch.