Normality of meromorphic functions and their differential polynomials

In this paper, we study the normality of meromorphic families and prove the following theorem: Let k be a positive integer, P(z) be a non-constant polynomial satisfying P (0) = 0, h(not equivalent to 0) be a holomorphic function in a domain D, H(f, f' ,..., f((k))) be a differential polynomial with Gamma/gamma vertical bar(H) < k + 1, and F be a meromorphic family in D. If, for each f is an element of F, f not equal 0 and P (f((k)))+ H(f , f',..., f((k))) not equal h for z is an element of D, then F is a normal family in D.