Bohr phenomenon for subordinating families of certain univalent functions

By B. Bhowmik, Nilanjan Das. Journal of Mathematical Analysis and Applications, 2018

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Abstract In this article we develop an elegant method to compute sharp Bohr radius for subordination classes of certain univalent functions.

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Bohr radius for certain classes of starlike and convex univalent functions (2020, background): “[13] Let f and g be anlytic in D with Taylor expansions (1.”
Sharp Bohr type inequality (2020, background): “See for example, [8–11, 14–20, 25–27, 30, 33, 35] and the recent survey on this topic by AbuMuhanna et al.”
On the Bohr inequality with a fixed zero coefficient (2019, background): “[7] Let f(z) and g(z) be two analytic functions in D such that f(z) = ∑ ∞ k=0 akz , and g(z) = ∑ ∞ k=0 bkz .”
Improved Bohr's phenomenon in quasi-subordination classes (2019, background): “kr = X∞ n=0 |an| 2r2n ≤ kgk r = X∞ n=0 |bn| 2r2n for all r ∈ [0,1) and therefore, since a0 = Φ0b0, we have (8) kf0kr ≤ |b0| 2(1− |Φ 0| 2)+kg 0kr for all r ∈ [0,1). The desired inequality follows from (6), (7) and (8). The radius 1/3 is sharp as can be seen by setting Φ = 1 and ω(z) = z. The followin”
Bohr phenomenon for certain subclasses of harmonic mappings (2020, background): “In 2018, Bhowmik and Das [13] studied the Bohr radius for the class of concave univalent functions with openinig angle πα, 1 ≤ α ≤ 2 and also obtained the Bohr radius for the class of starlike functions of order α, for 0 ≤ α ≤ 1/2.”