Open Access

Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces

Fixed Point Theory and Applications20082008:167535

DOI: 10.1155/2008/167535

Received: 13 January 2008

Accepted: 3 May 2008

Published: 7 May 2008


Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping), and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a solution of certain variational inequality provided that the sequence satisfies and , for some and the sequence is asymptotically regular.

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Authors’ Affiliations

Department of Mathematics, Dong-A University


© Jong Soo Jung. 2008

This article is published under license to BioMed Central Ltd. 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.