The theory of normality family plays an important role in the research of value distribution theory. Now, combining the normality family with the shared values or shared functions is an important topic in the normality family theory. In this paper , based on Nevanlinna's value distribution and used the Zalcman's lemma and Hurwitz's theorem, we obtain some general normal criterias for the meromorphic functions which concern the shared values,and improve some existed results.
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