Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces
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 asym...
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/48035 |
| Online Access: | http://hdl.handle.net/11441/48035 https://doi.org/10.1016/j.na.2013.03.018 |
| Access Level: | Open access |
| Keyword: | Averaged mapping Firmly nonexpansive mapping Convex feasibility problem Geodesic space Asymptotic regularity Proof mining |
| Summary: | 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. |
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