Open Access

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

Fixed Point Theory and Applications20052005:359216

Received: 10 September 2003

Published: 30 June 2005


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

Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
Department of Mathematics, Faculty of Sciences, King Abdul Aziz University, Jeddah, Saudi Arabia


© Chidume et al. 2005