Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 528614, 10 pages
doi:10.1155/2008/528614
Convergence to compact sets of inexact orbits of nonexpansive mappings in Banach and metric spaces
Evgeniy Pustylnik
, Simeon Reich
and Alexander J. Zaslavski
Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel
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.