Towards Viscosity Approximations of Hierarchical Fixed-point Problems

  title={Towards Viscosity Approximations of Hierarchical Fixed-point Problems},
  author={Abdellatif Moudafi and P.-E. Maing{\'e}},
We introduce methods which seem to be a new and promising tool in hierarchical fixedpoint 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… CONTINUE READING


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Publications referenced by this paper.
Showing 1-7 of 7 references

The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings

I. Yamada
Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Elsevier, New York • 2001
View 4 Excerpts
Highly Influenced

Variational Analysis

R. Tyrrell Rockafellar, Roger J-B Wets
View 1 Excerpt
Highly Influenced

Variational Convergence for Functions and Operators

H. Attouch
Applicable Mathematics Series, Pitman, Massachusetts • 1984
View 1 Excerpt

Two remarks on the convergence of convex functions and monotone operators

P.-L. Lions
Nonlinear Analysis. Theory, Methods and Applications 2 • 1978

Two remarks on the convergence of convex functions and monotone operators , Nonlinear Analysis

H.-K. Xu
Theory , Methods and Applications • 1978

Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert

H. Brézis
North-Holland Mathematics Studies, no. 5, North-Holland, Amsterdam; American Elsevier, New York • 1973
View 1 Excerpt

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