Geodesic
On univalent log-harmonic mappings
Filomat, Tome 36 (2022) no. 12, p. 4211

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DOI

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. Growth and distortion theorems for certain special subclasses of log-harmonic mappings are studied. Finally, we propose two conjectures, namely, log-harmonic coefficient and log-harmonic covering conjectures.
DOI : 10.2298/FIL2212211L
Classification : 30C35, 30C45, 35Q30
Keywords: Schwarz function, harmonic and univalent log-harmonic mappings, log-harmonic right half-plane mappings, coefficient estimates, growth and distortion theorems, log-harmonic coefficient conjecture 
Zhihong Liu; Saminathan Ponnusamy. On univalent log-harmonic mappings. Filomat, Tome 36 (2022) no. 12, p. 4211 . doi: 10.2298/FIL2212211L
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     author = {Zhihong Liu and Saminathan Ponnusamy},
     title = {On univalent log-harmonic mappings},
     journal = {Filomat},
     pages = {4211 },
     year = {2022},
     volume = {36},
     number = {12},
     doi = {10.2298/FIL2212211L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2212211L/}
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