Improved Bohr's inequality for locally univalent harmonic mappings

Antti Rasila; Saminathan Ponnusamy; Stavros Evdoridis

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Improved Bohr's inequality for locally univalent harmonic mappings

Stavros Evdoridis, Saminathan Ponnusamy, Antti Rasila

Complex Variables · Submitted 26 Sep 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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 $|g'(z)|\le|h'(z)|$.

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arXiv ID1709.08944 (version 1)

Pith IDGJWXTAZI, Pith's permanent record of this paper and its review

CitationAntti Rasila, Saminathan Ponnusamy, Stavros Evdoridis. "Improved Bohr's inequality for locally univalent harmonic mappings." arXiv:1709.08944 (2017). https://pith.science/paper/GJWXTAZI

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.85 · mentions code or data availability 0.01.

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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 $|g'(z)|\le|h'(z)|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. \cite{KayPon2}, 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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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 $\|g'(z)\|\le\|h'(z)\|$.	contribution 0.85	0.96	0.86	asserted 1.00
s1	The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. \cite{KayPon2}, 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.	method 0.88	0.75	0.22	asserted 1.00
s2	In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.	contribution 0.80	0.93	0.10	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original 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 $|g'(z)|\le|h'(z)|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. \cite{KayPon2}, 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.

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Cites as background 3 papers

Other recent results on this topic include [ref] .

Bohr inequality for odd analytic functions · Introduction and Preliminaries · 0.98
Other recent results on this topic include [ref] .

Bohr's inequality for analytic functions $\sum_k b_k z^{kp+m}$ and harmonic functions · Introduction and Preliminaries · 0.98
Other recent results on this topic include [ref] .

Bohr--Rogosinski radius for analytic functions · Introduction and Preliminaries · 0.98

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