Krasnoselskii-mann method for multi-valued non-self mappings in CAT(0) spaces

We define Mann iterative scheme in CAT(0) spaces and obtain Δ-convergence and strong convergence of the iterative scheme to a fixed point of multi-valued nonexpansive non-self mappings. We also obtain strong convergence of the scheme to a fixed point of multi-valued quasi-nonexpansive non-self mappings under appropriate conditions. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.