Fixed Point Theory and Applications
Volume 2005 (2005), Issue 2, Pages 233-241
doi:10.1155/FPTA.2005.233

Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings

C. E. Chidume,1 Habtu Zegeye,1 and Naseer Shahzad2

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.

Abstract

Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti:K→E, i=1,…,r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K 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 Ti, i=1,2,…,r, satisfy some mild conditions.