Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 95453, 10 pages

Towards viscosity approximations of hierarchical fixed-point problems

A. Moudafi and P.-E. Maingé

GRIMAAG, Département Scientifique interfacultaires, Université Antilles Guyane, Schelcher 97200, Martinique, France

Received 10 February 2006; Revised 14 September 2006; Accepted 18 September 2006

Copyright © 2006 A. Moudafi and P.-E. Maingé. 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 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, 0(IQ)x+NFixP(x), where NFixP denotes the normal cone to the set of fixed point of the original nonexpansive mapping P and Q a suitable nonexpansive mapping criterion. The link with other approximation schemes in this field is also made.