Normal Family of Meromorphic Functions concerning Shared Values. (30th January 2013)

• Record Type: Journal Article
• Authors: Chen, Wei; Tian, Honggen; Zhang, Yingying; Yuan, Wenjun
• Other Names: Li Bao Qin Academic Editor.
• Is Part Of: Journal of complex analysis. Volume 2013(2013)
• Publication Date: 2013-01-30
• Subjects: Functions of complex variables -- Periodicals; Mathematical analysis -- Periodicals; 515.905
• DOI: 10.1155/2013/107281
• Languages: English
• ISSNs: 2314-4963

Abstract

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.