Improved Bohr's phenomenon in quasi-subordination classes

TL;DR

This paper generalizes refined Bohr inequalities to quasi-subordination classes, extending previous results and providing new insights into the behavior of bounded analytic functions within this framework.

Contribution

It introduces a generalized 'distance form' version of Bohr's inequality applicable to quasi-subordination classes, unifying and extending prior refined results.

Findings

Extended Bohr inequalities to quasi-subordination classes

Derived new bounds in the reformulated 'distance form'

Unified majorization and subordination cases under a common framework

Abstract

Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and thereby we extend the refined versions of the Bohr inequality for the class of the quasi-subordinations which contains both the classes of majorization and subordination as special cases. As a consequence, we obtain several new results.