Normal Criterion Concerning Shared Values

Abstract EN

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/cfk-1)(f′)k(z)+f(z)≠bfk/cfk-1 or (1/cfk-1)(f′)k(z)+f(z)=bfk/cfk-1⇒f(z)=bf, then F is normal.

These results improve some earlier previous results.