Quantcast

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

Research paper by CE Chidume, Habtu Zegeye, Naseer Shahzad

Indexed on: 30 Jun '05Published on: 30 Jun '05Published in: Fixed Point Theory and Applications



Abstract

Let Open image in new window be a nonempty closed convex subset of a reflexive real Banach space Open image in new window which has a uniformly Gâteaux differentiable norm. Assume that Open image in new window is a sunny nonexpansive retract of Open image in new window with Open image in new window as the sunny nonexpansive retraction. Let Open image in new window, Open image in new window, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of Open image in new window 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 Open image in new window, Open image in new window, satisfy some mild conditions.