Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces

2014/10/05 by Hossein Dehghan, Dehghan, Hossein, Jamal Rooin +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Fixed Point Theorems Analysis #Optimization and Variational Analysis #math.FA

paper · pdf · doi:10.48550/arxiv.1410.1137

Accepted in Journal of Nonlinear and Convex Analysis

arxiv created 2014/10/05 · arxiv updated 2014/10/07

Abstract

For a nonempty convex subset C of a Hadamard space X, it is proved that u=P_Cx if and only if ⟨\overrightarrowxu,\overrightarrowuy⟩ \geqslant0 for all y∈ C. As an application of this characterization, we prove strong convergence of two iterative algorithms with perturbations for nonexpansive mappings.

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