Bohr-type inequalities for unimodular bounded analytic functions

TL;DR

This paper generalizes Bohr-type inequalities for bounded analytic functions in the unit disk by introducing a parameterized sequence, extending previous results and broadening the scope of these inequalities.

Contribution

It introduces a new parameterized approach to Bohr inequalities, generalizing earlier results for bounded analytic functions in the unit disk.

Findings

Established new versions of Bohr inequalities with parameterized sequences

Generalized previous results on Bohr inequalities

Extended applicability to a broader class of functions

Abstract

In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series representations of the functions involved with the Bohr sum and thereby introducing a single parameter, which generalize several related results of earlier authors.