In this paper, we first define a new kind of mappings involving a finite family of accretive operators via resolvents. We show some properties of such mappings in Banach spaces. Then we introduce a new iteration method using these mappings to find the common zeros of two finite families of accretive operators. Our next move is to prove the some strong convergence theorems under appropriate conditions in real reflexive strictly convex Banach spaces having uniformly Gateaux differentiable norm. Finally, we give some applications of our main results