- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Meromorphic functions sharing 1CM+1IM concerning periodicities and shifts Bull. Korean Math. Soc. 2019 Vol. 56, No. 1, 45-56 https://doi.org/10.4134/BKMS.b180076Published online 2019 Jan 31 Xiao-Hua Cai, Jun-Fan Chen Fujian Normal University; Fujian Province University 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. Keywords : meromorphic function, shared value, periodicity, shift, unique\-ness MSC numbers : 30D35, 30D30 Full-Text :