Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 68616, 10 pages
Convergece Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings
1Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italy
2Department of Mathematical Sciences, Bayero University, Kano, Nigeria
Received 20 October 2006; Revised 30 January 2007; Accepted 31 January 2007
Academic Editor: Donal O'Regan
Copyright © 2007 C. E. Chidume and Bashir Ali. 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.
Let be a real Banach space, a closed convex nonempty subset of , and asymptotically quasi-nonexpansive mappings with sequences (resp.)
satisfying as , and . Let
be a sequence in . Define a sequence by , , , , , . Let . Necessary and sufficient conditions for a strong convergence of the sequence to a common fixed point of the family are proved. Under some appropriate conditions, strong and weak convergence theorems are also proved.