Some unity results on entire functions and their difference operators related to 4 CM theorem

Abstract

Abstract This paper is to consider the unity results on entire functions sharing two values with their difference operators and to prove some results related to 4 CM theorem. The main result reads as follows: Let f ( z ) $f(z)$ be a nonconstant entire function of finite order, and let a 1 $a_{1}$ , a 2 $a_{2}$ be two distinct finite complex constants. If f ( z ) $f(z)$ and Δ η n f ( z ) $\Delta _{\eta }^{n}f(z)$ share a 1 $a_{1}$ and a 2 $a_{2}$ “CM”, then f ( z ) ≡ Δ η n f ( z ) $f(z)\equiv \Delta _{\eta }^{n} f(z)$ , and hence f ( z ) $f(z)$ and Δ η n f ( z ) $\Delta _{\eta }^{n}f(z)$ share a 1 $a_{1}$ and a 2 $a_{2}$ CM.

Keywords

• Entire functions
• Differences
• Shared values
• Nevanlinna theory