Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings
© Chidume et al. 2005
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.