A Note on the value distribution of a differential monomial and some normality criteria

TL;DR

This paper establishes new value distribution results for differential monomials that lead to improved criteria for the normality of families of analytic functions.

Contribution

It introduces novel value distribution theorems that enhance existing normality criteria for analytic functions.

Findings

Improved normality criteria for families of analytic functions.

Enhanced value distribution results for differential monomials.

Refinement of recent theoretical results in the field.

Abstract

In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.