Shared Values and Normal Families of Meromorphic Functions

Normal families of meromorphic functions sharing values or functions

* Correspondence: jiangyunbo@ss. buaa.edu.cn School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, People’s Republic of China Abstract In this paper, we investigate the normal families of meromorphic functions concerning shared values and shared analytic functions and prove some normal criteria that generalize or extend some results obtained by Q. C. Zhang, Y....

Normal Criteria for Families of Meromorphic Function concerning Shared Values

Let k be a positive integer and let F be a family of meromorphic functions in the plane domain D all of whose zeros with multiplicity at least k. Let P = apz p + · · ·+a2z +z be a polynomial, ap, a2 6= 0 and p = deg(P ) ≥ k+2. If, for each f, g ∈ F , P (f)G(f) and P (g)G(g) share a non-zero constant b in D, where G(f) = f (k) + H(f) be a differential polynomial of f satisfying w deg |H ≤ k l+1 ...

A Note on Normal Families of Meromorphic Functions Concerning Shared Values

Fixed Points of Composite Meromorphic Functions and Normal Families

We show that there exists a function f meromorphic in the plane C such that the family of all functions g holomorphic in the unit disk D for which f ◦ g has no fixed point in D is not normal. This answers a question of Hinchliffe who had shown that this family is normal if Ĉ\f(C) does not consist of exactly one point in D. We also investigate the normality of the family of all holomorphic funct...

Some Normal Criteria for Families of Meromorphic Functions

In the paper, we study the normality of families of meromorphic functions related a Hayman Conjecture. We consider whether a family meromorphic functions F is normal in D, if for each function f in F , f ′ + af = b has at most one zero, where n is a positive integer, a and b = 0 are two finite complex numbers. Some examples show that the conditions in our results are best possible.