Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces

Abstract

For a nonempty convex subset $C$ of a Hadamard space $X$, it is proved that $u=P_{C}x$ if and only if $⟨\overrightarrow{xu},\overrightarrow{uy}⟩⩾0$ for all $y\in C$. As an application of this characterization, we prove strong convergence of two iterative algorithms with perturbations for nonexpansive mappings.

Accepted in Journal of Nonlinear and Convex Analysis