An extension of one direction in Marty's normality criterion

TL;DR

This paper extends Marty's normality criterion by replacing the spherical derivative with a more general measure involving higher derivatives, broadening the theorem's applicability.

Contribution

It introduces a novel extension of Marty's theorem, incorporating higher derivatives into the normality criterion.

Findings

Generalization of Marty's theorem to higher derivatives

Broader conditions for normality of families of functions

Potential applications in complex analysis

Abstract

We prove an extension of one direction in Marty's theorem where the spherical derivative is replaced by a more general quantity involving higher derivatives.