The solution by iteration of nonlinear equations in uniformly smooth Banach spaces

Let E be a uniformly smooth Banach space and let T: D(T) subset of E --> E be a strong pseudocontraction with an open domain D(T) in E and a fixed point x* is an element of D(T). We establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to the fixed point of T. Related results deal with the iterative solution of operator equations of the forms f is an element of Tx and f is an element of x + lambda Tx, lambda > 0, when T is a set-valued strongly accretative operator. Our theorems include the cases in which the operator T is defined only locally. Explicit error estimates are also given. (C) 1997 Academic Press.