Strong convergence of an iterative algorithm for accretive operators and nonexpansive mappings

In this paper, an iterative algorithm for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping is considered in a uniformly convex Banach space having a weakly continuous duality mapping. Under suitable control conditions, strong convergence of the sequence generated by proposed algorithm to a common point of two sets is established. The main theorems develop and complement the recent results announced by researchers in this area.