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Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces

Opened Access Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces

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Autor: Nicolae, Adriana
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2013-08
Publicado en: Nonlinear Analysis: Theory, Methods and Applications, 87, 102-115.
Tipo de documento: Artículo
Resumen: We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates. We use methods of proof mining to obtain an explicit quantitative version of a generalization to geodesic spaces of a result on the asymptotic behavior of Picard iterates for firmly nonexpansive mappings proved by Reich and Shafrir. From this result we obtain effective uniform bounds on the asymptotic regularity for firmly nonexpansive mappings. Besides this, we derive effective rates of asymptotic regularity for sequences generated by two algorithms used in the study of the convex feasibility problem in a nonlinear setting.
Cita: Nicolae, A. (2013). Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces. Nonlinear Analysis: Theory, Methods and Applications, 87, 102-115.
Tamaño: 251.9Kb
Formato: PDF

URI: http://hdl.handle.net/11441/48035

DOI: 10.1016/j.na.2013.03.018

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