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Erratum to: Hyperbolic Distortion, Boundary Behaviour and Finite Blaschke Products

Erratum to: Hyperbolic Distortion, Boundary Behaviour and Finite Blaschke Products Comput. Methods Funct. Theory (2015) 15:289–290 DOI 10.1007/s40315-015-0112-4 ERRATUM Erratum to: Hyperbolic Distortion, Boundary Behaviour and Finite Blaschke Products Nina Zorboska Published online: 25 March 2015 © Springer-Verlag Berlin Heidelberg 2015 Erratum to: Comput. Methods Funct. Theory DOI 10.1007/s40315-014-0099-2 This errata note is a correction to Proposition 2.2 in the original version of the paper. We provide here a corrected statement of the result with its corrected proof. The proposition requires an additional assumption of univalence, since the proof uses a result from [1, p. 71] which requires it. Note that the result in [1, p. 71] does require the univalence, even though it has been stated there without this assumption. Proposition 2.2 Let φ be a univalent self-map of D, and let ζ ∈ ∂ D be such that lim τ (z) = 0. Then there exists , an open subarc of ∂ D containing the point ζ , z→ζ φ such that the only possible subsets of  mapped by φ into ∂ D are sets of measure zero. Proof Since lim τ (z) = 0, for any 0 < < 1, ∃δ> 0 such that τ (z)< z→ζ φ φ whenever z ∈ B(ζ, δ) ∩ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Erratum to: Hyperbolic Distortion, Boundary Behaviour and Finite Blaschke Products

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-015-0112-4
Publisher site
See Article on Publisher Site

Abstract

Comput. Methods Funct. Theory (2015) 15:289–290 DOI 10.1007/s40315-015-0112-4 ERRATUM Erratum to: Hyperbolic Distortion, Boundary Behaviour and Finite Blaschke Products Nina Zorboska Published online: 25 March 2015 © Springer-Verlag Berlin Heidelberg 2015 Erratum to: Comput. Methods Funct. Theory DOI 10.1007/s40315-014-0099-2 This errata note is a correction to Proposition 2.2 in the original version of the paper. We provide here a corrected statement of the result with its corrected proof. The proposition requires an additional assumption of univalence, since the proof uses a result from [1, p. 71] which requires it. Note that the result in [1, p. 71] does require the univalence, even though it has been stated there without this assumption. Proposition 2.2 Let φ be a univalent self-map of D, and let ζ ∈ ∂ D be such that lim τ (z) = 0. Then there exists , an open subarc of ∂ D containing the point ζ , z→ζ φ such that the only possible subsets of  mapped by φ into ∂ D are sets of measure zero. Proof Since lim τ (z) = 0, for any 0 < < 1, ∃δ> 0 such that τ (z)< z→ζ φ φ whenever z ∈ B(ζ, δ) ∩

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 25, 2015

References