Open Access Research Article

Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces

Tomonari Suzuki

Author Affiliations

Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Kitakyushu, Tobata 804-8550, Japan

Fixed Point Theory and Applications 2006, 2006:59692  doi:10.1155/FPTA/2006/59692


The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2006/1/59692


Received: 19 August 2005
Revisions received: 24 February 2006
Accepted: 26 February 2006
Published: 1 June 2006

© 2006 Suzuki

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .

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