Open Access

Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces

Fixed Point Theory and Applications20062006:69758

https://doi.org/10.1155/FPTA/2006/69758

Received: 27 June 2005

Accepted: 28 November 2005

Published: 1 March 2006

Abstract

Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let be a nonempty closed convex subset of , and let be a uniformly continuous pseudocontraction. If is any contraction map on and if every nonempty closed convex and bounded subset of has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers , , that the iteration process , , , strongly converges to the fixed point of , which is the unique solution of some variational inequality, provided that is bounded.

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Authors’ Affiliations

(1)
Department of Mathematics, Statistics, & Computer Science, University of Port Harcourt

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Copyright

© Aniefiok Udomene. 2006

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.