International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1643-1653
doi:10.1155/IJMMS.2005.1643
Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces
Hafiz Fukhar-Ud-Din1
and Abdul Rahim Khan2
1Department of Mathematics, Islamia University, Bahawalpur 63100, Pakistan
2Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Abstract
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.