Bohr type inequality for {C}es\'{a}ro and {B}ernardi integral operator on simply connected domain

TL;DR

This paper investigates Bohr type inequalities for Cesàro and Bernardi integral operators acting on analytic functions within simply connected domains, extending classical results beyond the unit disk.

Contribution

It introduces new Bohr inequalities for these operators on more general simply connected domains, broadening the scope of classical Bohr phenomena.

Findings

Established Bohr inequalities for Cesàro operator

Derived Bohr inequalities for Bernardi integral operator

Extended classical Bohr results to broader domains

Abstract

In this article, we study the Bohr type inequality for {C}es\'{a}ro operator and {B}ernardi integral operator acting on the space of analytic functions defined on a simply connected domain containing the unit disk $\mathbb{D}$.