Let E be an arbitrary real Banach space and let
$A:D(A)\subseteq E\mapsto E\>$ be a Lipschitz strongly K-accretive operator.
It is proved that modified iteration processes of the Mann and Ishikawa
types converge strongly to the unique solutions of the operator equations
$Ax=f\>$ and $Kx+Ax=f\>$ where $f\in E\>$ is an arbitrary but fixed vector.