Chinese Quarterly Journal of Mathematics ›› 2011, Vol. 26 ›› Issue (3): 394-399.

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Normal Families of Holomorphic Functions Concerning Shared a Polynomial 

  

  1. 1. College of Mathematics, Honghe University2. College of Mathematics and Computing Science, Changsha University of Science and Technology 

  • Received:2008-04-02 Online:2011-09-30 Published:2023-04-19
  • About author:LIU Zhi-hong(1978-), male, native of Shaoyang, Hunan, a lecturer of Honghe University, M.S.D., engages in complex analysis.
  • Supported by:
    Supported by the Scientific Research Starting Foundation for Master and Ph.D.of Honghe University(XSS08012); Supported by Scientific Research Fund of Yunnan Provincial Education Department of China Grant(09C0206);

Abstract: In this paper, we study normal families of holomorphic function concerning shared a polynomial. Let F be a family of holomorphic functions in a domain D, k(2) be a positive integer, K be a positive number and α(z) be a polynomial of degree p(p>1). For each f∈F and z∈D, if f and f sharedα(z)CM and |f(k)(z)|<K whenever f(z)-α(z)=0 in D, then F is normal in D.

Key words: holomorphic functions, normal family, shared values, polynomial

CLC Number: