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arXiv · 1410.1137

Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces

Hossein Dehghan·Jamal Rooin
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Abstract

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.

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Hossein Dehghan, Jamal Rooin. 2014-10-05. Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces. https://arxiv.org/abs/1410.1137

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