Meromorphic functions sharing 1CM+1IM concerning periodicities and shifts
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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 $c\in\mathbb{C}\backslash\{0\}$, and let $a_1$, $a_2$ be two distinct finite complex numbers. Suppose that $\mu\left(f\right)\neq1$, $\rho_2\left(f\right)<1$, 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.
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 $c\in\mathbb{C}\backslash\{0\}$, and let $a_1$, $a_2$ be two distinct finite complex numbers. Suppose that $\mu\left(f\right)\neq1$, $\rho_2\left(f\right)<1$, 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.
참고문헌 (19)
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