Chinese Quarterly Journal of Mathematics ›› 2011, Vol. 26 ›› Issue (3): 360-365.

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A Note on Normal Families of Meromorphic Functions and Sharing Set

  

  1. 1. Department of Mathematics, Xinjiang Normal University 2. Shaozhou Normal College, Shaoguan University  3. School of Mathematics and Information Science, Guangzhou University 
  • Received:2010-09-03 Online:2011-09-30 Published:2023-04-18
  • About author:XIAO Bing(1960-), male, native of Urumgi, Xinjiang, a lecturer of Xinjiang Normal University, M.S.D., engages in complex analysis and its applications; WU Qi-feng(corresponding author)(1963-), male, native of Shaoguan, Guangdong, an associate professor of Shaoguan University, M.S.D., engages in complex analysis and statistics; YUAN Wen-jun(1957-), male, native of Anyue, Sichuan, a professor of Guangzhou University, Ph.D., engages in complex analysis and its applications.
  • Supported by:
    Supported by the NSF of China(10771220); Supported by the Doctorial Point Fund of National Education Ministry of China(200810780002);

Abstract: In the paper, we prove the main result: Let k(≥2) be an integer, and a, b and c be three distinct complex numbers. Let F be a family of functions holomorphic in a domain D in complex plane, all of whose zeros have multiplicity at least k. Suppose that for each f∈F, f(z) and f(k)(z) share the set {a,b,c}. Then F is a normal family in D.

Key words: entire function, normal family, meromorphic function, share value set

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