A Value Distribution Result and Some Normality Criteria using Partial Sharing of Small Functions

TL;DR

This paper generalizes a value distribution theorem and develops new normality criteria for families of functions using partial sharing of small functions, improving existing results in complex analysis.

Contribution

It introduces a generalized value distribution result and enhances normality criteria, broadening their applicability in complex analysis.

Findings

Generalized a key value distribution theorem.

Proved new normality criteria using partial sharing.

Improved and extended existing normality results.

Abstract

In this paper, we first generalize a value distribution result of Lahiri and Dewan [4] and as an application of this result we prove a normality criterion using partial sharing of small functions. Further, in sequel normality criteria of Hu and Meng [3] and Ding, Ding and Yuan [1] are improved and generalized when the domain $D:=\{z:|z|<R,0<R\leq\infty\}$.