Refined Bohr-type inequalities with area measure for bounded analytic functions

TL;DR

This paper introduces five new sharp Bohr-type inequalities for bounded analytic functions in the unit disk, using Schwarz functions to generalize previous results and enhance the understanding of coefficient bounds.

Contribution

The paper presents novel sharp Bohr-type inequalities incorporating Schwarz functions, extending and generalizing earlier results in the field of bounded analytic functions.

Findings

Established five new sharp inequalities for bounded analytic functions.

Generalized previous results by incorporating Schwarz functions.

Enhanced the theoretical framework of Bohr-type inequalities.

Abstract

In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the functions involved and thereby, we generalize several related results of earlier authors.