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. Su ppose T: E --> E is a continuous (not necessarily Lipschitzian) strong ly accretive map such that (I - T) has bounded range, where I denotes the identity operator. It is proved that the Ishikawa iterative sequen ce converges strongly to the unique solution of equation Tx = f, f is an element of E. Our results extend and complement the recent results obtained by Chidume. (C) 1997 Academic Press.