Summary: In this paper, we prove some properties of fixed point set of fundamentally non-expansive mappings and derive the existence of fixed point theorems as follows results of [H. Salahifard, S. M. Vaezpour and S. Dhompongsa, “Fixed point theorems for some generalized nonexpansive mappings in CAT(0) spaces”, J. Nonlinear Anal. Optim. 4, No. 2, 241–248 (2013), http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/243] in hyperbolic spaces.