Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MEROMORPHIC FUNCTIONS SHARING 1CM+1IM CONCERNING PERIODICITIES AND SHIFTS

  • Cai, Xiao-Hua (Department of Mathematics Fujian Normal University) ;
  • Chen, Jun-Fan (Department of Mathematics Fujian Normal University)
  • Received : 2018.01.25
  • Accepted : 2018.05.30
  • Published : 2019.01.31
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Abstract

The aim of this paper is to investigate the problems of meromorphic functions sharing values concerning periodicities and shifts. In this paper we prove the following result: Let f(z) and g(z) be two nonconstant entire functions, let $c{\in}{\mathbb{C}}{\setminus}\{0\}$, and let $a_1$, $a_2$ be two distinct finite complex numbers. Suppose that ${\mu}(f){\neq}1$, ${\rho}_2(f)<1$, and f(z) = f(z+c) for all $z{\in}{\mathbb{C}}$. If f(z) and g(z) share $a_1$ CM, $a_2$ IM, then $f(z){\equiv}g(z)$. Moreover, examples are given to show that all the conditions are necessary.

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