ON UNIVALENT LOG-HARMONIC MAPPINGS

Zhihong Liu, Saminathan Ponnusamy

Abstract


We consider the class of univalent log-harmonic mappings on the unit disk.Firstly, we present general idea of constructing log-harmonic Koebe mappings, log-harmonic right half-plane mappings and log-harmonic two-slits mappings and then we show precise ranges of these mappings. Moreover, coefficient estimates for univalent log-harmonic starlike mappings are obtained. Finally, we propose two conjectures, namely, log-harmoniccoefficient and log-harmonic covering conjectures.

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