On the uniqueness of meromorphic functions that share small functions on annuli

Abstract

In this paper, we aim to investigate the uniqueness of meromorphic functions that share small functions on annuli. As a matter of fact, we give several uniqueness theorems about meromorphic functions sharing four or three distinct small functions on the annulus $\mathbb{A}=\{z:\frac{1}{R_{0}}<|z|<R_{0}\},$ where $1<R_{0}\leq+\infty.$ To some extent, our theorems extend the previous work by T. B. Cao, H. X. Yi and H. Y. Xu, and also generalize the work by N. Wu and Q. Ge.

Keywords

• uniqueness
• meromorphic functions
• transcendental
• annuli
• sharing small functions