Let E be a real Banach space and let A be an m-accretive operator with a zero.Define a sequence {xn} as follows: xn,+1=αnf(xn) + (1-αn)Jrnxn, where {αn}, {rn} are sequences satisfying certain conditions, and Jr denotes the resolvent (I+rA)-1 for r 1. Strong convergence of the algorithm {xn} is obtained provided that E either has a weakly continuous duality map or is uniformly smooth.