Improved Bohr's inequality for locally univalent harmonic mappings

Evdoridis, Stavros; Ponnusamy, Saminathan; Rasila, Antti

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Improved Bohr's inequality for locally univalent harmonic mappings

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Title:	Improved Bohr's inequality for locally univalent harmonic mappings
Author(s):	Evdoridis, Stavros ; Ponnusamy, Saminathan ; Rasila, Antti
Date:	2018-10-09
Language:	en
Pages:	201-213
Department:	Department of Mathematics and Systems Analysis Indian Institute of Technology, Madras Israel Institute of Technology
Series:	INDAGATIONES MATHEMATICAE: NEW SERIES, Volume 30, issue 1
ISSN:	0019-3577
DOI-number:	10.1016/j.indag.2018.09.008
Subject:	111 Mathematics
Keywords:	111 Mathematics
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Citation: Evdoridis , S , Ponnusamy , S & Rasila , A 2018 , ' Improved Bohr's inequality for locally univalent harmonic mappings ' INDAGATIONES MATHEMATICAE: NEW SERIES , vol. 30 , no. 1 , pp. 201-213 . DOI: 10.1016/j.indag.2018.09.008
Abstract: We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form f=h+\overline{g}, where h is bounded by 1 and \|g'(z)\| \leq \|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.

Permanent link to this item: http://urn.fi/URN:NBN:fi:aalto-201901141087 Email this Export to RefWorks QR Code Print BibTex Tweet