Bohr type inequalities for functions with a multiple zero at the origin

TL;DR

This paper refines Bohr's inequality for functions with a multiple zero at the origin, addressing a specific open question and extending the classical results in this specialized setting.

Contribution

It provides a refined version of Bohr's inequality tailored for functions with multiple zeros at the origin, partially answering an open question from prior research.

Findings

Refined Bohr's inequality for functions with multiple zeros at the origin

Partial resolution of an open question in the field

Extension of classical Bohr's phenomenon to new function classes

Abstract

Recently, there has been a number of good deal of research on the Bohr's phenomenon in various setting including a refined formulation of his classical version of the inequality. Among them, in \cite{PaulPopeSingh-02-10} the authors considered the cases in which the above functions have a multiple zero at the origin. In this article, we present a refined version of Bohr's inequality for these cases and give a partial answer to a question from \cite{PaulPopeSingh-02-10} for the revised setting.