Bohr--Rogosinski radius for analytic functions

Ilgiz R Kayumov; Saminathan Ponnusamy

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arXiv · 1708.05585

Bohr--Rogosinski radius for analytic functions

Ilgiz R Kayumov·Saminathan Ponnusamy

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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 radii for analytic functions defined for $|z|<1$. Also, we prove several different improved versions of the classical Bohr's inequality. Finally, we also discuss the Bohr-Rogosinski's radius for a class of subordinations. All the results are proved to be sharp.

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Ilgiz R Kayumov, Saminathan Ponnusamy. 2017-08-18. Bohr--Rogosinski radius for analytic functions. https://arxiv.org/abs/1708.05585

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