Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 95453, 10 pages
doi:10.1155/FPTA/2006/95453

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

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, 0∈(I−Q)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.