Weak stability of the Ishikawa iteration procedures for ∅-hemicontractions and accretive operators Original Research Article

Let X be an arbitrary Banach space, K be a nonempty closed convex subset of X, and T : K → K be a Lipschitzian and hemicontractive mapping with the property lim inft→∞(∅(t)/t) > 0. It is shown that the Ishikawa iteration procedures are weakly T-stable. As consequences, several related results deal with the weak stability of these procedures for the iteration proximation of solutions of nonlinear equations involving accretive operators. Our results improve and extend those corresponding results announced by Osilike.