Bohr Phenomenon for Certain Close-to-Convex Analytic Functions

Abstract

We say that a class G of analytic functions f of the form f(z)=?n=0?anzn in the unit disk D: = { z? C: | z| < 1 } satisfies a Bohr phenomenon if for the largest radius Rf< 1 , the following inequality ?n=1?|anzn|?d(f(0),?f(D))holds for | z| = r? Rf and for all functions f? G. The largest radius Rf is called Bohr radius for the class G. In this article, we obtain the Bohr radius for certain subclasses of close-to-convex analytic functions. We establish the Bohr phenomenon for certain analytic classes Sc?(?),Cc(?),Cs?(?),Ks(?) and obtain the radius Rf such that the Bohr phenomenon for these classes holds for | z| = r? Rf. As a consequence of these results, we obtain several interesting corollaries about the Bohr phenomenon for the aforesaid classes. � 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.