Fixed Point Theory and Applications
Volume 2005 (2005), Issue 2, Pages 233-241
Convergence theorems for a common fixed point of a finite family
of nonself nonexpansive mappings
1Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italy
2Department of Mathematics, Faculty of Sciences, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Received 10 September 2003; Revised 6 July 2004
Copyright © 2005 C. E. Chidume et al. 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 nonempty closed convex subset of a reflexive real Banach space which has a uniformly Gâteaux differentiable norm. Assume that is a sunny nonexpansive retract of with as the sunny nonexpansive retraction. Let , , be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that , , satisfy some mild conditions.