Univalent harmonic mappings with two preassigned values

In this paper we consider a class ) of normalized harmonic functions which map the unit disk onto starlike domains. We give necessary and sufficient condition for ∈ ), distortion bounds and extreme points. We partially solve the problem of the Koebe set for ). We also consider the Schild’s Conjectur...

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Bibliographic Details
Published inDemonstratio mathematica Vol. 42; no. 4; pp. 711 - 722
Main Author Gregorczyk, Magdalena
Format Journal Article
LanguageEnglish
Published De Gruyter Open 01.12.2009
Subjects
30C45
harmonic mappings
Koebe set
Montel type normalization
Schild’s conjecture
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Summary:In this paper we consider a class ) of normalized harmonic functions which map the unit disk onto starlike domains. We give necessary and sufficient condition for ∈ ), distortion bounds and extreme points. We partially solve the problem of the Koebe set for ). We also consider the Schild’s Conjecture for the class of harmonic mappings.
ISSN:2391-4661
2391-4661
DOI:10.1515/dema-2013-0209