Uniformly locally univalent harmonic mappings
The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family B H ( λ ) of uniformly locally univalent harmonic mappings. Finally, we show that the subclass...
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| Veröffentlicht in: | Proceedings of the Indian Academy of Sciences. Mathematical sciences 2018-06, Vol.128 (3), p.1-14, Article 32 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family
B
H
(
λ
)
of uniformly locally univalent harmonic mappings. Finally, we show that the subclass of
k
-quasiconformal harmonic mappings in
B
H
(
λ
)
and the class
B
H
(
λ
)
are contained in the Hardy space of a specific exponent depending on
λ
, respectively, and we also discuss the growth of coefficients for harmonic mappings in
B
H
(
λ
)
. |
|---|---|
| ISSN: | 0253-4142 0973-7685 |
| DOI: | 10.1007/s12044-018-0405-4 |