Improved Bohr’s inequality for locally univalent harmonic mappings

By Stavros Evdoridis, Saminathan Ponnusamy, Antti Rasila. Indagationes mathematicae, 2017

82 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6d64d835263b44b266ca9289cc4c1942c85dd8e0

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the Bohr inequality with a fixed zero coefficient (2019, background): “[15] have presented several improved versions of Bohr’s inequality for harmonic mappings.”
Bohr phenomenon for certain subclasses of harmonic mappings (2020, background): “For more intriguing aspects of Bohr phenomenon we refer to [5, 11, 12, 19, 26, 31] and the references therein.”
Improved Bohr's phenomenon in quasi-subordination classes (2019, result): “See also recent works from [3,4,6,9,11,13–17] and the references therein.”
Sharp Bohr type inequality (2020, methodology): “For a harmonic analog of Bohr’s inequality (1) and that of Theorem A, we refer to [22] and [27], respectively.”
Bohr Type Inequalities for Functions with a Multiple Zero at the Origin (2020, methodology): “ve and in turn the uniqueness of the solution ρk(a). To prove the sharpness of this upper bound, we again use the function (7), but here we ﬁx a ∈ [0,1]. In this case we get for the left hand side of (10) (for simplicity call it as BohrInequalityincaseofamultiplezero 9 B(r)) the term B(r) = ark + rk”
Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings (2019, unknown): “For certain other results on harmonic Bohr’s inequality, we refer to [9, 16].”
Bohr radius for certain classes of starlike and convex univalent functions (2020, background): “Bohr phenomenon for harmonic mappings has also been extensively studied by several authors (see [4, 11, 17, 23, 24, 26, 30]).”