Metric projection and convergence theorems for nonexpansive mappings in   Hadamard spaces
  For a nonempty convex subset $C$ of a Hadamard space $X$, it is proved that $u=P_Cx$ if and only if $\langle\overrightarrow{xu},\overrightarrow{uy}\rangle \geqslant0$ for all $y\in C$. As an application of this characterization, we prove strong convergence of two iterative algorithms with perturbations for nonexpansive mappings. 
Hossein Dehghan and Jamal Rooin
math.FA