This thesis studies the normal families and uniqueness of meromorphic functions and get some results by using Nevanlinna's value distribution. With regard to uniqueness of meromorphic functions, the author study a problem on sharing a small function and generalize the result of Fang. M. L. and Wei. H. In normal families of meromorphic functions, the author studies the normal families of meromorphic functions concerning differentional polynomials and fix-point, sharing value. The results obtained in the dissertation perfect and generalize the present conclusions.
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