ITERATIVE SOLUTIONS OF NONLINEAR ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES

Suppose E is an arbitrary real Banach space and K is a nonempty closed convex and
bounded subset of E. Suppose T : K —>• K is a uniformly continuous strong pseudocontraction.
It is proved that the Mann and the Ishikawa iteration methods converge
strongly to the unique fixed point of T. Furthermore, our results also hold for the slightly
more general class of strictly hemicontractive maps. Related results deal with the iterative
approximation of solutions of accretive operator equations in arbitrary real Banach spaces.