Bohr radius for certain classes of starlike and convex univalent functions

Abstract

We say that a class F consisting of analytic functions f(z)=∑n=0∞anzn in the unit disk D:={z∈C:|z|<1} satisfies a Bohr phenomenon if there exists rf∈(0,1) such that∑n=1∞|anzn|≤d(f(0),∂f(D)) for every function f∈F and |z|=r≤rf, where d is the Euclidean distance. The largest radius rf 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.