The Properties And Criterion Of Normal Functions And α-normal Functions

The central problem of the normal family is to look for a newly and brief normal criterion,that is the sufficient and necessary condition of the function family.The normal functions are also quite important in the theory of normal family.Let D={z:|z|<1} be a unit disk on the complex plan,Aut(D) denotes the set of functions which are one-one conformal mapping on D,if f(z)is meronorphic function on D,then f(z)is normal function if and only if the func-tions family(?)={fog:g∈Aut(D)} is normal family.Corresponding to the normal family,In this thesis we investigate the property and criterion of normal family,use the method in analogy to Pang's generalization of Zalcman's lemma, we get a new crition of narmal functions and strongly normal functions,At the same time,we also consider the property and crition ofα-normal functions and stronglyα-normal fuanctions at given aα,0<α<∞.