  Let f be a non constant meromorphic function and a(not identically zero or
infinity) be a meromorphic function satisfying T(r,a) = o(T(r,f)) as r tends to
infinity, and p(z) be a polynomial of degree n greater than or equal to 1 with
p(0) = 0. Let P[f] be a non constant differential polynomial of f. Under
certain essential conditions, we prove the uniqueness of p(f) and P[f] when
p(f) and P[f] share a with weight l greater than or equal to zero. Our result
generalizes the results due to Zang and Lu, Banerjee and Majumder, Bhoosnurmath
and Kabbur and answers a question of Zang and Lu.
