International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1685-1692
doi:10.1155/IJMMS.2005.1685
Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Received 21 October 2004; Revised 20 April 2005
Copyright © 2005 Somyot Plubtieng and Rabian Wangkeeree. 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
Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:C→C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative
scheme converges strongly to some fixed point of T.