Global iteration schemes for strongly pseudo-contractive maps

Suppose is a real uniformly smooth Banach space, is a nonempty closed convex and bounded subset of , and is a strong pseudo-contraction. It is proved that if has a fixed point in then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in , converge strongly to the unique fixed . No continuity assumption is necessary for this convergence. Moreover, our iteration parameters are independent of the geometry of the underlying Banach space and of any property of the operator.