Convergence theorems for nonexpansive semigroups in CAT(0) spaces

Let C be a convex and compact subset of a CAT(0) space X. In this paper, we consider the following iterative scheme for a one-parameter nonexpansive semigroup {T(t):t≥0} on C: {x1∈C,xn+1=λT(tn)xn⊕(1−λ)xn, where λ∈(0,1) and {tn}⊂[0,∞), and we prove that, under certain conditions, {xn} converges to a common fixed point of the semigroup {T(t):t≥0}.