Some variable Krasnonsel'skiĭ-Mann iteration algorithms generate some sequences {xn}, {yn}, and  {zn}, respectively, via the formula xn+1=(1-αn)xn+αnTN⋯T2T1xn, yn+1=(1-βn)yn+βn∑i=1NλiTiyn, zn+1=(1-γn+1)zn+γn+1T[n+1]zn, where T[n]=Tn mod N and the mod function takes values in {1,2,…,N}, {αn}, {βn}, and  {γn} are sequences in (0,1), and {T1,T2,…,TN} are sequences of nonexpansive mappings. We will show, in a fairly general Banach space, that the sequence {xn}, {yn}, {zn} generated by the above formulas converge weakly to the common fixed point of {T1,T2,…,TN}, 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.