Normal Family of Meromorphic Functions concerning Shared Values. (30th January 2013) - Chen, Wei; Tian, Honggen; Zhang, Yingying; Yuan, Wenjun
Abstract : 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.