Let $E$ be a real Banach space and let $A$ be an $m$-accretive operator with a zero. Define a sequence $\{x_n\}$ as follows: $x_{n+1}=\alpha_n f(x_n)+(1-\alpha_n)J_{r_n}x_n$, where $\{\alpha_n\}$, $\{r_n\}$ are sequences satisfying certain conditions, and $J_r$ denotes the resolvent $(I+rA)^{-1}$ for $r>1$. Strong convergence of the algorithm $\{x_n\}$ is obtained provided that $E$ either has a weakly continuous duality map or is uniformly smooth.
