Convergence theorems for nonexpansive semigroups in View the MathML sourceCAT(0) spaces

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