An Extension of a Normality Result by Carath\'eodory

TL;DR

This paper extends Carathéodory's fundamental normality test by exploring shared functions, providing a broader understanding of normality in complex analysis.

Contribution

It introduces a novel extension of Carathéodory's normality result focusing on shared functions, expanding the theoretical framework.

Findings

Extended the normality test to shared functions

Provided new conditions for normality in complex functions

Enhanced understanding of function sharing in complex analysis

Abstract

We extend the fundamental normality test due to Carath\'eodory in the sense of shared functions.