Geodesic
Stability of the Iteration Method for non Expansive Mappings
Serdica Mathematical Journal, Tome 22 (1996) no. 3, pp. 331-340.

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The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.
Keywords: Convex Minimization, Convergence, Iteration Method, Gradient Method, Monotone Inclusions, Prox Method, Stability 
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     author = {Lemaire, B.},
     title = {Stability of the {Iteration} {Method} for non {Expansive} {Mappings}},
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Lemaire, B. Stability of the Iteration Method for non Expansive Mappings. Serdica Mathematical Journal, Tome 22 (1996) no. 3, pp. 331-340. http://geodesic.mathdoc.fr/item/SMJ2_1996_22_3_a3/