Volume 3,  Issue 1, 2002

Article 3



E-Mail: EPSEELON@aol.com

Received 14 May, 2001; accepted 17 July, 2001.
Communicated by: S.S. Dragomir

ABSTRACT.    Let $E$ be a real Banach Space and $K$ a nonempty closed convex (not necessarily bounded) subset of $E$. Iterative methods for the approximation of fixed points of asymptotically demicontractive mappings $T:K \rightarrow K$ 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, $1 < q < \infty$, 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 $K$ 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.

Key words:
Asymptotically Demicontractive Maps, Fixed Points, Modified Mann and Ishikawa Iteration Methods with Errors

2000 Mathematics Subject Classification:
47H06, 47H10, 47H15, 47H17.

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