Open Access

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

Fixed Point Theory and Applications20052005:359216

https://doi.org/10.1155/FPTA.2005.233

Received: 10 September 2003

Published: 30 June 2005

Abstract

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.

Authors’ Affiliations

(1)
Mathematics Section, The Abdus Salam International Centre for Theoretical Physics
(2)
Department of Mathematics, Faculty of Sciences, King Abdul Aziz University

Copyright

© Chidume et al. 2005