Bohr radius for certain classes of starlike and convex univalent functions

By V. Allu, H. Halder. Journal of Mathematical Analysis and Applications, 2020

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Abstract We say that a class F consisting of analytic functions f ( z ) = ∑ n = 0 ∞ a n z n in the unit disk D : = { z ∈ C : | z | 1 } satisfies a Bohr phenomenon if there exists r f ∈ ( 0 , 1 ) such that ∑ n = 1 ∞ | a n z n | ≤ d ( f ( 0 ) , ∂ f ( D ) ) for every function f ∈ F and | z | = r ≤ r f , where d is the Euclidean distance. The largest radius r f is the Bohr radius for the class F . In this paper, we establish the Bohr phenomenon for the classes consisting of Ma-Minda type starlike functions and Ma-Minda type convex functions as well as for the class of starlike functions with respect to a boundary point.

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