Suppose
E
E
is a real uniformly smooth Banach space,
K
K
is a nonempty closed convex and bounded subset of
E
E
, and
T
:
K
→
K
T:K\to K
is a strong pseudo-contraction. It is proved that if
T
T
has a fixed point in
K
K
then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in
K
K
, converge strongly to the unique fixed
T
T
. 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.