Normal Criterion Concerning Shared Values

Abstract

We study normal criterion of meromorphic functions shared values, we obtain the following. LetFbe a family of meromorphic functions in a domainD, such that functionf∈Fhas zeros of multiplicity at least 2, there exists nonzero complex numbersbf,cfdepending onfsatisfying(i)  bf/cfis a constant;  (ii)min {σ(0,bf),σ(0,cf),σ(bf,cf)≥m}for somem>0;  (iii)  (1/cfk-1)(f′)k(z)+f(z)≠bfk/cfk-1or(1/cfk-1)(f′)k(z)+f(z)=bfk/cfk-1⇒f(z)=bf, thenFis normal. These results improve some earlier previous results.