Normality criteria for a family of meromorphic functions with multiple zeros

TL;DR

This paper establishes new normality criteria for families of meromorphic functions with multiple zeros, extending previous results by sharing holomorphic functions through differential polynomials.

Contribution

It introduces generalized normality criteria for meromorphic functions with multiple zeros, involving sharing holomorphic functions via differential polynomials, broadening earlier findings.

Findings

Normality criteria for meromorphic functions with multiple zeros

Extension of Fang, Zalcman, and Chen et al.'s results

Conditions involving sharing holomorphic functions by differential polynomials

Abstract

In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some of the results of Fang and Zalcman and Chen et al to a great extent.