Article
Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings
Author/s | Domínguez Benavides, Tomás
Lorenzo Ramírez, Josefa |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2001 |
Deposit Date | 2016-09-22 |
Published in |
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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 ... 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. |
Funding agencies | Dirección General de Investigación Científica y Técnica (DGICYT). España Junta de Andalucía |
Project ID. | PB 96-1338-C01-C02
FQM 0127 |
Citation | 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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