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  • Research Article
  • 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:

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, Trieste, 34014, Italy
(2)
Department of Mathematics, Faculty of Sciences, King Abdul Aziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

Copyright

© Chidume et al. 2005

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