The Bohr inequality for the generalized C{\'e}saro averaging operators

TL;DR

This paper generalizes the classical Bohr theorem and applies it to the generalized Cesàro averaging operators, extending the theorem's scope within complex analysis.

Contribution

It introduces a generalized Bohr inequality and establishes a Bohr-type theorem for the generalized Cesàro operator, broadening the understanding of such inequalities.

Findings

Proved a generalized Bohr inequality.

Established a Bohr theorem for the generalized Cesàro operator.

Extended classical results to a broader operator class.

Abstract

The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Ces\'aro operator.