Normal Criteria For Families Of Meromorphic Functions Concerning Differential Polynomials

Since1907P.Montel proposed the concept of normal family so far,normal fam-ilies theory has made great progress for the important position of the theory in the field of complex dynamic system.Now it has become an important branch of complex analysis.On the basis of previous studies the author studies on the families of mero-morphic functions concerning several forms of differential polynomials,and gets several conclusions.First,the author studies on the family of meromorphic functions whose poles and zeros of multiplicity at least k,and the differential polynomials of form G(f)=P(f)f-n meet certain conditions.If every two functions of the family with their form of G(f) sharing a nonzero finite complex number a,then the family is normal.Next the author studies on the two families of holomorphic functions g,g whose zeros of multiplcity at least k,where g is normal.If for every function in g,corresponding there is a function in g,and their differential polynomial forms of f(f(k))n sharing a nonzero finite complex number a,then g is normal.Finally,the author gets a normal criterion concerning sharing a moving target,For a family of meromorphic functions whose poles of multiplicity large enough in D,if any two functions in the family with their derivative of k-th order share a moving target,then the family is normal in D.