Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Copyright © 2009 S. Imnang and S. Suantai. 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 introduce a general iteration scheme for a finite family
of generalized asymptotically quasi-nonexpansive mappings in Banach spaces.
The new iterative scheme includes the multistep Noor iterations with errors,
modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and
Noor, and Khan and Takahashi scheme as special cases. Our results generalize
and improve the recent ones announced by Khan et al. (2008),
H. Fukhar-ud-din and S. H. Khan (2007), J. U. Jeong and S. H. Kim (2006),
and many others.