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Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

 

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Opened Access Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings
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Author: Domínguez Benavides, Tomás
Lorenzo Ramírez, Josefa
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2001
Published in: Proceedings of the American Mathematical Society, 129 (12), 3549-3557.
Document type: Article
Abstract: Let X be a Banach space, C a weakly compact convex subset of X and T : C → C an asymptotically nonexpansive mapping. Under the usual assumptions on X which assure the existence of fixed point for T, we prove that the set of fixed points is a nonexpansive retract of C. We use this result to prove that all known theorems about existence of fixed point for asymptotically nonexpansive mappings can be extended to obtain a common fixed point for a commuting family of mappings. We also derive some results about convergence of iterates.
Cite: Domínguez Benavides, T. y Lorenzo Ramírez, J. (2001). Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings. Proceedings of the American Mathematical Society, 129 (12), 3549-3557.
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URI: http://hdl.handle.net/11441/45286

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