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http://dx.doi.org/10.5666/KMJ.2022.62.2.243

Bohr's Phenomenon for Some Univalent Harmonic Functions  

Singla, Chinu (Department of Mathematics, Sant Longowal Institute of Engineering and Technology)
Gupta, Sushma (Department of Mathematics, Sant Longowal Institute of Engineering and Technology)
Singh, Sukhjit (Department of Mathematics, Sant Longowal Institute of Engineering and Technology)
Publication Information
Kyungpook Mathematical Journal / v.62, no.2, 2022 , pp. 243-256 More about this Journal
Abstract
In 1914, Bohr proved that there is an r0 ∈ (0, 1) such that if a power series ∑∞m=0 cmzm is convergent in the open unit disc and |∑∞m=0 cmzm| < 1 then, ∑∞m=0 |cmzm| < 1 for |z| < r0. The largest value of such r0 is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.
Keywords
Bohr radius; harmonic univalent functions; convex in one direction;
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