Several Problems In Relation To Normal Family Theory Of Meromorphic Functions

In section 1,the author introduce some fundamental results and some notations.In section 2,the author study the normality of a familiy of holomorphic and meromophic functions concerning one shared values.Four general normal criterions are obtained, which improves the results given by Zhang Q. C.[ 25 ], f′is replaced by f ( k). Theorem 1 Let n ,k be two positive integers with n≥k+ 3. F be a family of functions meromorphic on a domain D ,all of whose zeros have multiplicity at least k + 1.Suppose that each pair of functions f and g in F , f ( k )? afnand g ( k )? agn share a value b on D , where a ,bare two finite constants such that a≠0.Then F is normal on D .We obtain the theorem 1-4.In section 3, the author study the normality of a famility of holomorphic functions and meromorphic functions concerning the exceptional value.Five general normal criterions are obtained.We obtain the theorem 5-6.