Academic Editor: S. Reich
Copyright © 2010 Huimin He et al. This is an open access article distributed under the
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Some variable Krasnonsel'skiĭ-Mann iteration algorithms generate some sequences , , and, respectively, via the formula , , , where and the mod function takes values in , , , and are sequences in and are sequences of nonexpansive mappings. We will show, in a fairly general Banach space, that the sequence , , generated by the above formulas converge weakly to the common fixed point of , respectively. These results are used to solve the multiple-set split feasibility problem recently introduced by Censor et al. (2005). The purpose of this paper is to introduce convergence theorems of some variable Krasnonsel'skiĭ-Mann iteration algorithms in Banach space and their applications which solve the multiple-set split feasibility problem.