Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 528614, 10 pages
doi:10.1155/2008/528614
Research Article
Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces
Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel
Received 27 September 2008; Accepted 17 November 2008
Academic Editor: Brailey Sims
Copyright © 2008 Evgeniy Pustylnik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the influence of computational errors on the convergence to compact sets of orbits of nonexpansive mappings in Banach and metric spaces. We first establish a convergence theorem assuming that the computational errors are summable and then provide examples which show that the summability of errors is necessary for convergence.