In a real uniformly convex and p-uniformly smooth Banach space, a modified forward-backward splitting iterative algorithm is presented, where the computational errors and the superposition of perturbed operators are considered. The iterative sequence is proved to be convergent strongly to zero point of the sum of infinite m-accretive mappings and infinite [Formula: see text]-inversely strongly accretive mappings, which is also the unique solution of one kind variational inequalities. Some new proof techniques can be found, especially, a new inequality is employed compared to some of the recent work. Moreover, the applications of the newly obtained iterative algorithm to integro-differential systems and convex minimization problems are exemplified.
Keywords: [Formula: see text]-inversely strongly accretive mapping; [Formula: see text]-strictly pseudo-contractive mapping; [Formula: see text]-strongly accretive mapping; p-uniformly smooth Banach space; perturbed operator.