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Firmly nonexpansive mappings in classes of geodesic spaces

 

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Opened Access Firmly nonexpansive mappings in classes of geodesic spaces
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Author: Ariza Ruiz, David
Leustean, Laurentiu
López Acedo, Genaro
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2014
Published in: Transactions of the American Mathematical Society, 366 (8), 4299-4322.
Document type: Article
Abstract: Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations.
Cite: Ariza Ruiz, D., Leustean, L. y López Acedo, G. (2014). Firmly nonexpansive mappings in classes of geodesic spaces. Transactions of the American Mathematical Society, 366 (8), 4299-4322.
Size: 278.7Kb
Format: PDF

URI: http://hdl.handle.net/11441/42604

DOI: 10.1090/S0002-9947-2014-05968-0

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