Akademik Veri Yönetim Sistemi
Ukrainian Mathematical Journal, cilt.64, sa.5, ss.653-671, 2012 (SCI-Expanded, Scopus)
Let ℂ be the complex plane, let ̄ℂ = ℂ ∪ {∞}, let G ⊂ ℂ be a finite Jordan domain with 0 ∈ G, let L:= ∂G; let Ω:= ̄ℂ\̄G, and let w = φ(z) be a conformal mapping of G onto a disk B(0, ρ0):= {w: {pipe}w{pipe} < ρ0} normalized by the conditions φ(0) = 0 and φ′(0)=1, where ρ0 = ρ0(0, G) is the conformal radius of G with respect to 0. Let and let πn,p(z) be the generalized Bieberbach polynomial of degree n for the pair (G, 0) that minimizes the integral in the class of all polynomials of degree deg Pn ≤ n such that Pn(0) = 0 and P′n(0) = 1. We study the uniform convergence of the generalized Bieberbach polynomials πn,p(z) to φp(z) on ̄G with interior and exterior zero angles determined depending on properties of boundary arcs and the degree of their tangency. In particular, for Bieberbach polynomials, we obtain improved estimates for the rate of convergence in these domains. © 2012 Springer Science+Business Media New York.