In this paper, a three-step implicit iteration process with errors
is introduced and we prove strong convergence theorem of the new
scheme with some mild conditions on the real sequences to a common fixed point of nite family of asymptotically $phi$--demicontractive
mappings defined on a closed convex subset of a Banach space. The
new scheme includes several well known explicit and implicit iterative
schemes and the results in this paper extend, compliment and improve
several strong convergence results in the literature to the class of map-
pings considered in our work.