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We provide a new proof technique to obtain strong convergence of the sequences generated by viscosity iterative methods for a Rockafellar-type iterative algorithm and a Halpern-type iterative algorithm to a zero of an accretive operator in Banach spaces. By using a new method different from previous ones, the main results improve and develop the recent well-known results in this area.

Some results on Rockafellar-type iterative algorithms for zeros of accretive operators