A further result on normal families and exceptional functions

Let k >= 3 be a positive integer, A > 1 be a constant, and ?(z)(equivalent to 0) be a function holomorphic in a domain D , and let F be a family of meromorphic functions defined in D. If, for every function f is an element of F, f has only zeros of multiplicity at least k and satisfies: (a) f(z) = 0 -> |f((k))(z)|<= A|?(z)|, (b) f ((k))(z) &NOTEQUexpressionL; ?(z), (c) all poles off have multiplicity at least 2 for k >= 4(3 for k = 3), then F is normal in D.