Let E be a real reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and C be a closed convex nonempty subset of E . Strong convergence theorems for approximation of a common zero of a countably infinite family of m -accretive mappings from C to E are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudocontractive mappings.