We study the influence of errors on the convergence of infinite products of nonexpansive mappings in metric spaces. Previously, certain convergence results were proved under the assumption that all exact orbits converge uniformly on the whole space. In the present paper, we improve upon these results by proving the convergence of inexact orbits only assuming uniform convergence of exact orbits on bounded subsets of the metric space. We also provide applications to the convex feasibility problem in Hilbert space.
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Simeon Reich, Alexander J. Zaslavski, Asymptotic Behavior of Inexact Infinite Products of Nonexpansive Mappings in Metric Spaces. Z. Anal. Anwend. 33 (2014), no. 1, pp. 101–117DOI 10.4171/ZAA/1501