Shared values and normal families of meromorphic functions

In this paper, we study the normality of a family of meromorphic functions concerning shared values and prove the following theorem: Let F be a family of meromorphic functions in a domain D, let k greater than or equal to 2 b e a positive integer, and let a, b, c be complex numbers such that a not eq ual b. If, for each f is an element of F, f and f((k)) share a and b in D, and the zeros of f(z) - c are of multiplicity greater than or equal to k 1, then F is normal in D. (C) 2001 Academic Press.