Bohr--Rogosinski radius for analytic functions

TL;DR

This paper introduces and investigates Bohr-Rogosinski radii for analytic functions in the unit disk, providing new sharp inequalities and exploring their behavior under subordination.

Contribution

It is the first to study Bohr-Rogosinski radii, offering improved inequalities and analyzing their sharpness and subordination properties.

Findings

Established sharp Bohr-Rogosinski radii for analytic functions.

Derived improved versions of classical Bohr's inequality.

Analyzed the radii for functions under subordination.

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.