In this paper we derive the following results:Let T be a family of holomorphic functions on a domain D, all of whose zeros have multiplicity at least k+1. Suppose that for each f∈(?), f(k)(z)= z(?)f(z)=1, then T is normal on D.Let (?) be a family of meromorphic functions on a domain D c C, all of whose zeros have multiplicity at least k+1, where k≥1 be a positive integer. If for any function f∈(?),(1)f=∞(?)f#≤M, where M> 0 be a constant;(2)f(k)≠1, then (?) is normal on D.
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