Bohr-Rogosinski Inequalities for bounded analytic functions

TL;DR

This paper refines and improves Bohr-Rogosinski inequalities for bounded analytic functions by incorporating area measures, enhancing understanding of these functions' behavior within the unit disk.

Contribution

It introduces improved versions of Bohr-Rogosinski inequalities for the class of bounded analytic self-maps, considering area measures of sub-disks.

Findings

Enhanced inequalities for analytic self-maps

Incorporation of area measure improves bounds

Provides sharper estimates for function behavior

Abstract

In this article, we analyze refined and improved versions of the classical Bohr inequality for the function class $\mathcal{B}$, which consists of analytic self-mappings defined on the unit disk $\mathbb{D}$. We improve the Bohr-Rogosinski inequality for the class $\mathcal{B}$ of analytic self-maps by incorporating the area measure of sub-disks $\mathbb{D}_r$ in $\mathbb{D}$.