Abstract
In this paper, we propose and analyze a three-step general iteration method which is a special case of an iteration method proposed in (S. Thianwan and S. Suantai, Convergence criteria of a new three-step iteration with errors for nonexpansive nonself-mappings, Comput. Math. Appl. 52 (2006), 1107-1118). Here we intend to study directly the accumulation, estimation and control of random errors in the newly proposed general iteration method. We give conditions under which the accumulated-error in our iteration method is bounded and controllable in a permissible range.
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