Common solutions to a system of variational inequalities over the set of common fixed points of demi-contractive operators

Eslamian, Mohammad

Comptes Rendus. Mathématique, Tome 355 (2017) no. 11, pp. 1168-1177.

Dans cette Note, nous introduisons un algorithme parallèle explicite, trouvant les solutions communes d'un système d'inégalités variationnelles sur l'ensemble des points fixes communs à une famille finie d'opérateurs semi-contractants. Sous des hypothèses convenables, nous démontrons la convergence forte de cet algorithme dans le cadre des espaces de Hilbert. Les résultats obtenus étendent et améliorent ceux de Tian et Jiang (2017), de Censor, Gibali et Reich (2012), ainsi que de plusieurs autres auteurs.

In this paper, we introduce an explicit parallel algorithm for finding common solutions to a system of variational inequalities over the set of common fixed points of a finite family of demi-contractive operators. Under suitable assumptions, we prove the strong convergence of this algorithm in the framework of a Hilbert space. The results obtained in this paper extend and improve the results of Tian and Jiang (2017), of Censor, Gibali and Reich (2012), and of many others.

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