This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Colao, VittorioLaurent¸iu Leu¸stean, Laurent¸iu Leu¸steanGenaro L´opez, Genaro L´opezMart´ın-M´arquez, Victoria2019-06-2820091864-7596https://doi.org/10.34657/1945https://oa.tib.eu/renate/handle/123456789/2536Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.application/pdfeng510Nonexpansive mappingiterative algorithmfixed pointviscosity approximationuniformly smooth Banach spacerates of asymptotic regularityproof miningvariational inequality problemaccretive operatorReport