Iterative Solution of Nonlinear Equations Involving Strongly Accretive Operators without the Lipschitz Assumption

LetEbe a real Banach space with a uniformly convex dual spaceE*. SupposeT:E → Eis a continuous (not necessarily Lipschitzian) strongly accretive map such that (I − T) has bounded range, whereIdenotes the identity operator. It is proved that the Ishikawa iterative sequence converges strongly to the unique solution of equationTx = f,f ∈ E. Our results extend and complement the recent results obtained by Chidume.