Bohr--Rogosinski radius for analytic functions

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.

13 pages; It is with the journal

References in corpus (1)

• Bohr inequality for odd analytic functions

Cited by in corpus (6)

• Refined Bohr inequality for bounded analytic functions
• Bohr operator on analytic functions
• Generalization of Bohr-type inequality in analytic functions
• The Bohr-type operator on analytic functions and sections
• Note on Improved Bohr Inequality for harmonic mappings
• Multidimensional analogues of refined Bohr's inequality