Some Results On The Normal Family Of Meromorphic Functions

By using the Nevanlinna value distribution theory and Pang-Zalcman lemma this thesis studies the normal families of meromorphic functions related to the exceptional values and the exceptional functions, which generalizes the results due to L.Yang-G.H.Zhang[22] and X.Z.Wu[8] in some extent and obtains the following two results.Theorem 1:Let F be a family of meromorphic functions defined on D, k be positive integer and h,m,,l be positive integers or oo. If for every f∈F, the zeros of f have multiplicities at least h,the poles of f have multiplicities at least l,the zeros of have multiplicities at least m, where ai(z) (i=0,…, k-1) is a holomorphic function in D, and then F is normal on D.Theorem 2:Let F be a family of meromorphic functions defined on D, k be positive integer and h,m,,l be positive integers or oo, d be natural number.Let φ((?) 0) be a holomorphic function in D and φ has only zeros with multiplicities at most d. If for every f∈F, the zeros of f have multiplicities at least h, the poles of f have multiplicities at least l, the zeros of differential polynomial have multiplicities at least m, where ai(z) (i=0,…, k-1)is a holomorphic function in D, and φ and f have no commom zero, then F is normal on D.