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