Normal Families Of Meromorphic Functions Concerning Differential Polynomials And Shared Values

The core of the theory of normal families is the study of normality criteria. Inthis thesis, two normality criteria are proved. One is the normality criterion concerningdifferential polynomials: let F be a family of functions meromorphic in domain D,a = 0,b be two finite complex numbers and m,k,n be three positive integers suchthat n≥m + 1.be a differential polynomial, where deg(Mr)≥1 and ar is analytic in D for allr∈Ik. If for each f∈F, all zeros of f have multiplicity at least k + 1, andfm + a(f(k) + P[f])n = b in D, then F is normal in D.The other is the normality criterion concerning shared values: let n≥2,m,kbe three positive integers, and a be a non-zero complex number and F be a familyof meromorphic functions in domain D such that each f∈F has only zeros ofmultiplicity at least max{k, 2}. If for each pair of f and g in F, fm(f(k))n andgm(g(k))n share the value a IM, then F is normal in D.This thesis consists of six chapters. The first chapter introduces the thesis'study-ing work, studying purpose, background and so on. The second chapter introducesNevanllina's value distribution theory. The third chapter outlines the basic knowledgeand classic results. In the fifth and sixth chapters, we consider the above normalitycriteria, including their backgrounds, proofs, and so on. In last chapter, we give someopen questions.