Normal Criteria of Function Families 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 ...

Normal Criteria of Function Families Concerning Shared Values

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 ...

A Note on Normal Families of Meromorphic Functions Concerning Shared Values

Two New Criteria for Normal Families

Let a0, . . . , ak−1 be analytic functions on a domain Ω. Let F be a family of meromorphic functions f on Ω such that f 6= 0 and f (k) + ak−1f (k−1) + . . . + a0f 6= 0 on Ω, for all f ∈ F . Then {f ′/f : f ∈ F} is a normal family. Furthermore, let a0, . . . , ak−1 be meromorphic functions on a domain Ω. Let F be a family of meromorphic functions f on Ω such that f 6= 0, f ′ 6= 0 and f (k) + ak−...