Abstract
There are a number of articles which deal with Bohr's phenomenon whereas only a few papers appeared in the literature on Rogosinski's radii for analytic functions defined on the unit disk |z|<1. In this article, we introduce and investigate Bohr-Rogosinski's phenomenon for analytic functions defined for |z|<1 in a general setting. In addition we discuss and derive Bohr-Rogosinski's radii for Cesáro operators on the space of bounded analytic functions. Finally, we also obtain the Bohr-Rogosinski's radius for a class of subordinations. All the results are proved to be sharp.
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