Common fixed point results in CAT(0) spaces

Let XX be a complete CAT(0) space, TT be a generalized multivalued nonexpansive mapping, and tt be a single valued quasi-nonexpansive mapping. Under the assumption that TT and tt commute weakly, we shall prove the existence of a common fixed point for them. In this way, we extend and improve a number of recent results obtained by Shahzad (2009) [7] and [12], Shahzad and Markin (2008) [6], and Dhompongsa et al. (2005) [5].