Normal Family of Meromorphic Functions concerning Shared Values

Abstract EN

We obtain a normal criterion of meromorphic functions concerning, shared values.

Let ℱ be a family of meromorphic functions in a domain D and let k,n≥k+2 be positive integers.

Let a≠0,b be two finite complex constants.

If, for each f∈ℱ, all zeros of f have multiplicity at least k+1 and f+a(f(k))n and g+a(g(k))n share b in D for every pair of functions f,g∈ℱ, then ℱ is normal in D.

This result generalizes the related theorem according to Xu et al.

and Qi et al., respectively.

There is a gap in the proofs of Lemma 3 by Wang (2012) and Theorem 1 by Zhang (2008), respectively.

They did not consider the case of f(z) being zerofree.

We will fill the gap in this paper.