The Bohr-type operator on analytic functions and sections

TL;DR

This paper introduces refined Bohr-type inequalities involving area for bounded analytic functions and develops a Bohr-type operator on analytic functions and their sections.

Contribution

It presents new refined inequalities related to the Bohr phenomenon and introduces a novel Bohr-type operator on analytic functions and their sections.

Findings

Refined Bohr-type inequalities associated with area for bounded analytic functions.

Definition and analysis of a Bohr-type operator on analytic functions.

Establishment of properties of sections in the context of Bohr-type inequalities.

Abstract

In this paper, firstly we prove two refined Bohr-type inequalities associated with area for bounded analytic functions $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n}$ in the unit disk. Later, we establish the Bohr-type operator on analytic functions and sections.