@article{Fan2022, 
author = {Jinyu Fan and Mingliang Fang and Jianbin Xiao},
title = {Uniqueness of meromorphic functions concerning fixed points},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {12},
pages = {20490-20509},
keywords = {meromorphic function, entire function, unicity, fixed point},
url = {https://www.sciopen.com/article/10.3934/math.20221122},
doi = {10.3934/math.20221122},
abstract = {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−Θmin(k+6.5), if  Θmin≥2.5k+6.5, otherwise  n>3k+8, and let  (fn)(k) and  (gn)(k) share  z CM,  f and  g share  ∞ IM, then one of the following two cases holds: If  k=1, then either  f(z)=c1ecz2,  g(z)=c2e−cz2, where  c1,c2 and  c are three constants satisfying  4n2(c1c2)nc2=−1, or  f=tg for a constant  t such that  tn=1; if  k≥2, then  f=tg for a constant  t such that  tn=1. Our results extend and improve some results due to [8,9,19,24].}
}