A Note on Normal Families Concerning Nonexceptional Functions and Differential Polynomials

TL;DR

This paper investigates the normality of families of meromorphic functions with differential polynomials, providing improved, generalized conditions and demonstrating sharpness through examples.

Contribution

It introduces new, broader criteria for normality of meromorphic function families involving differential polynomials, extending recent results.

Findings

Enhanced conditions for normality of meromorphic functions

Generalization of previous theorems by Chen

Examples demonstrating the sharpness of results

Abstract

We study normality of a family of meromorphic functions, whose differential polynomials satisfy a certain condition, which significantly improves and generalizes some recent results of Chen (Filomat, 31(14) 2017, 4665-4671). Moreover, we demonstrate, with the help of examples, that the result is sharp.