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 
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/
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     author = {Lemaire, B.},
     title = {Stability of the {Iteration} {Method} for non {Expansive} {Mappings}},
     journal = {Serdica Mathematical Journal},
     pages = {331--340},
     year = {1996},
     volume = {22},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_1996_22_3_a3/}
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