Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 018909, 10 pages
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
1Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics/Statistics/Computer Science, University of Port Harcourt, PMB, Port Harcourt 5323, Nigeria
Received 21 April 2005; Revised 13 July 2005; Accepted 18 July 2005
Copyright © 2006 Naseer Shahzad and Aniefiok Udomene. 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.
Suppose is a nonempty closed convex subset of a real Banach
space . Let be two asymptotically
quasi-nonexpansive maps with sequences such that and , and . Suppose is generated iteratively by where and are real sequences in . It is proved that (a) converges strongly to some if and only if ; (b) if is uniformly convex and if either or is compact, then converges strongly to some . Furthermore, if is uniformly convex, either or is compact and is generated by , where , are bounded, are real sequences in such that and , are summable; it is established that the
sequence (with error member terms) converges strongly
to some .