Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (6): 1166-1170.

• Articles • Previous Articles     Next Articles

Normal Family of Holomorphic Functions

 HUANG Wen, XIE Ya-Sheng   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2011-07-11 Revised:2012-09-08 Online:2012-12-25 Published:2012-12-25
  • Supported by:

    国家自然科学基金(11071074)资助

Abstract:

Let F be a family of holomorphic functions in a domain D, m, k  be two positive integers, for every f(z)∈F, the zeros of f(z)  have multiplicity at least k and k≥3, the nunbers of zeros of are at most m and mk+1. If f(z)=0 ↔ f (k)(z)=1,  then F is normal on D. This confirms a conjecture of Pang-Zalcman partly.

Key words: Holomorphic functions, Normal families, Shared values

CLC Number: 

  • 30D35
Trendmd