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.;E¬E be a strong pseudocontraction with an open domain D T. in E and a fixed point x*gD 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 fgTx and fgxqlTx, l )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.