# Viscosity Approximation Methods for Fixed-Points Problems

@article{Moudafi2000ViscosityAM, title={Viscosity Approximation Methods for Fixed-Points Problems}, author={Abdellatif Moudafi}, journal={Journal of Mathematical Analysis and Applications}, year={2000}, volume={241}, pages={46-55} }

The aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed-point of a given nonexpansive self-mapping.

## 666 Citations

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In this paper, we introduce a new Viscosity algorithm for approximating an element in the intersection of the set of common solutions of monotone inclusion problems and common fixed points of family…

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The aim of this work is to consider an iterative method for a-strict pseudo-contractions. Strong convergence theorems are established in a real 2-uniformly smooth Banach space.

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In this paper, we introduce new implicit and an explicit iteration methods based on Krasnoselskii-Mann iteration method and a contraction for finding a fixed point of a nonexpansive self-mapping of a…

### Combination of the Hybrid Steepest-Descent Method and the Viscosity Approximation

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In the context of a general q-uniformly smooth Banach space, we will prove the convergence of a scheme which covers Yamada’s hybrid steepest-descent method and Moudafi’s viscosity approximation in…

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We improve the viscosity approximation process for approximation of a fixed point of a quasi-nonexpansive mapping in a Hilbert space proposed by Mainge (2010). An example beyond the scope of the…

## References

SHOWING 1-10 OF 20 REFERENCES

### Produits infinis de resolvantes

- Mathematics
- 1978

This paper is concerned with the convergence of the sequence χn=(I+λnA)−1χn−1 whereA is maximal monotone and λn>0. Various assumptions onA and λn are considered.

### Viscosity Solutions of Minimization Problems

- MathematicsSIAM J. Optim.
- 1996

It is proved, in a rather large setting, that the solutions of the approximate problems converge to a ``viscosity solution'' of the original problem, that is, a solution that is minimal among all the solutions with respect to some viscosity criteria.

### A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method

- Mathematics
- 1996

We study the asymptotic behavior of the solutions to evolution equations of the form 0 # u* (t)+f(u(t), =(t)); u(0)=u0, where [f (}, =): =>0] is a family of strictly convex functions whose minimum is…

### Asymptotic analysis of the exponential penalty trajectory in linear programming

- MathematicsMath. Program.
- 1994

The primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution, which converges exponentially fast to a particular dual optimal solution.

### Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

- Mathematics
- 1973

### Rafle par un Convexe Variable,’

- Seminaire d’Analyse Convexe, Montpeĺ lier, expose,
- 1971

### Problems of Fixed Point Theory in Hilbert and Banach Spaces

- Lecture