Normal criteria concerning sharing 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 ...

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....

On Uniqueness Theorems of Meromorphic Functions Concerning Weighted Sharing of Three Values

In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain a uniqueness theorem which improves those given by Ozawa, H. X. Yi, I. Lahiri, Q. C. Zhang, and others. Some examples are provided to show that the results in this paper are the best possible. 2000 Mathematics Subject Classification: 30D30, 30D35