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

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 A = :1R₀ < |z|< R₀\, where 1 < R₀≤+∞. 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.