International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1643-1653

Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces

Hafiz Fukhar-Ud-Din1,2 and Abdul Rahim Khan3

1Department of Mathematics, Islamia University, Bahawalpur 63100, Pakistan
2Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo 152-8552, Japan
3Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 13 March 2005

Copyright © 2005 Hafiz Fukhar-Ud-Din and Abdul Rahim Khan. 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.


We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappings is unbounded, (ii) the iterative sequence contains an error term.