Uniqueness of meromorphic functions concerning fixed points

In this paper, we study a uniqueness question of meromorphic functions concerning fixed points and mainly prove the following theorem: Let f and g be two nonconstant meromorphic functions, let n, k be two positive integers with n > 3k + 10.5 - theta(min)(k + 6.5), if theta(min) >= 2.5/k+6.5, otherwise n > 3k + 8, and let (f(n))((k)) and (g(n))((k)) share z CM, f and g share infinity IM, then one of the following two cases holds: If k = 1, then either f(z) = c(1)e(cz2), g(z) = c(2)e(-cz2), where c(1), c(2) and c are three constants satisfying 4n(2)(c(1)c(2))(n)c(2) = -1, or f = tg for a constant t such that t(n) = 1; if k >= 2, then f = tg for a constant t such that t(n) = 1. Our results extend and improve some results due to [8, 9, 19, 24].

Automated summary

In this paper, a uniqueness question of meromorphic functions concerning fixed points is studied, and a theorem is mainly proved. The results extend and improve previous research.