Open Access

Towards viscosity approximations of hierarchical fixed-point problems

Fixed Point Theory and Applications20062006:95453

DOI: 10.1155/FPTA/2006/95453

Received: 10 February 2006

Accepted: 18 September 2006

Published: 27 November 2006

Abstract

We introduce methods which seem to be a new and promising tool in hierarchical fixed-point problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality, , where denotes the normal cone to the set of fixed point of the original nonexpansive mapping and a suitable nonexpansive mapping criterion. The link with other approximation schemes in this field is also made.

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Authors’ Affiliations

(1)
GRIMAAG, Département Scientifique interfacultaires, Université Antilles Guyane, Schelcher

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Copyright

© A. Moudafi and P.-E. Maingé. 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.