Improved Bohr’s inequality for locally univalent harmonic mappings

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form f=h+g¯, where h is bounded by 1 and |g′(z)|≤|h′(z)|. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related...

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Veröffentlicht in:Indagationes mathematicae 2019-01, Vol.30 (1), p.201-213
Hauptverfasser: Evdoridis, Stavros, Ponnusamy, Saminathan, Rasila, Antti
Format: Artikel
Sprache:eng
Schlagworte:
Bounded analytic functions
Harmonic functions
Locally univalent functions and Bohr radius
Mapping
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Zusammenfassung:We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form f=h+g¯, where h is bounded by 1 and |g′(z)|≤|h′(z)|. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk D(0,r) under the mapping f is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2018.09.008