47H06,47H10,47H15,47H17.

Let be a real Banach Space and a nonempty closed convex (not necessarily bounded) subset of . Iterative methods for the approximation of fixed points of asymptotically demicontractive mappings are constructed using the more general modified Mann and Ishikawa iteration methods with errors.

Our results show that a recent result of Osilike [1] (which is itself a generalization of a theorem of Qihou [2]) can be extended from real q-uniformly smooth Banach spaces, , to arbitrary real Banach spaces, and to the more general Modified Mann and Ishikawa iteration methods with errors. Furthermore, the boundedness assumption imposed on the subset in ([1], [2]) are removed in our present more general result. Moreover, our iteration parameters are independent of any geometric properties of the underlying Banach space.