A Normality Criterion of Meromorphic Functions Concerning Shared Set

Some Normality Criteria of Meromorphic Functions

Let f be a nonconstant meromorphic function in the complex plane C. We shall use the standard notations in Nevanlinna’s value distribution theory of meromorphic functions such as T r, f , N r, f , and m r, f see, e.g., 1, 2 . The notation S r, f is defined to be any quantity satisfying S r, f o T r, f as r → ∞ possibly outside a set of E of finite linear measure. Let F be a family of meromorphi...

Normal Criterion Concerning Shared Values

We study normal criterion of meromorphic functions shared values, we obtain the following. Let F be a family of meromorphic functions in a domain D, such that function f ∈ F has zeros of multiplicity at least 2, there exists nonzero complex numbers bf , cf depending on f satisfying i bf/cf is a constant; ii min{σ 0, bf , σ 0, cf , σ bf , cf ≥ m} for some m > 0; iii 1/ck−1 f f ′ k z f z / b f/c ...

Uniqueness of Meromorphic Functions Concerning Differential Monomials

Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions   f z and   g z satisfy     1, 1, n n k k E f f E g g    , where k and n are tow positive integers satisfying 3 k  and 11 n  , then either     1 2 , cz cz z z f c e g c e    where 1 c , 2 c , c are three constants, satisfying   1 ...

A Note on Normal Families of Meromorphic Functions Concerning Shared Values

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 ...