Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (2): 540-545.

• Articles • Previous Articles     Next Articles

A Normal Criterion Concerning Shared Values

 HUANG Xiao-Jie, LIU Zhi-Xiu   

  1. Jiangxi Blue Sky University, Nanchang 330098|Nanchang Business College of Jiangxi Agricultural University, Nanchang 330013
  • Received:2007-06-28 Revised:2010-01-21 Online:2011-04-25 Published:2011-04-25
  • Supported by:

    江西蓝天学院青年基金项目(XYKJ10006)资助

Abstract:

Let F be a family of meromorphic functions on a plane domain D, let a, e be two finite complex numbers, and b, c, d be three nonzero finite complex numbers. If, for each F, all the zeros of f-e are of multiplicity at least k≥2, f(z)=a↔ (z)=a↔ f (k)(z)=b, and f(k)(z)=cf (k+1)(z)=d, then F is a normal family on D. The same result holds for k=1so long as b≠(n+1)c, n=1, 2….

Key words: Meromorphic, Normal family, Shared value

CLC Number: 

  • 30D35
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