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

Let E be a real Banach space with a uniformly convex dual space E*. Suppose T: EªE is a continuous not necessarily Lipschitzian. strongly accretive map such that IyT. has bounded range, where I denotes the identity operator. It is proved that the Ishikawa iterative sequence converges strongly to the unique solution of equation Txsf, fgE. Our results extend and complement the recent results obtained by Chidume.