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

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 $D:=\{z:|z|<R,0<R\leq\infty\}$.