Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 719631, 13 pages
doi:10.1155/2010/719631
Research Article

Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi-I-Nonexpansive Mapping in Banach Space

Farrukh Mukhamedov and Mansoor Saburov

Department of Computational & Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Malaysia

Received 31 August 2009; Accepted 6 December 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Farrukh Mukhamedov and Mansoor Saburov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.