NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH MULTIPLE VALUES

In this paper, we consider some normality criteria concerning multiple values. Let F be a family of meromorphic functions defined in a domain D. Let k be a positive integer and psi(z) not equivalent to 0, infinity be a meromorphic function in D. If, for each f is an element of F and z is an element of D, (1) f(z) not equal 0, and all of whose poles are multiple; (2) all zeros of f((k)) (z) - psi(z) have multiplicities at least k + 3 in D; (3) all poles of psi(z) have multiplicities at most k in D, then F is normal in D.