Artículo
New examples of subsets of c with the FPP and stability of the FPP in hyperconvex spaces
Autor/es | Espínola García, Rafael
Japón Pineda, María de los Ángeles Souza, Daniel |
Departamento | Universidad de Sevilla. Departamento de Análisis matemático |
Fecha de publicación | 2021-07-22 |
Fecha de depósito | 2021-11-25 |
Publicado en |
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Resumen | The purpose of this work is two-fold. On the one side, we focus on the space of real convergent sequences c where we study non-weakly compact sets with the fixed point property. Our approach brings a positive answer to a ... The purpose of this work is two-fold. On the one side, we focus on the space of real convergent sequences c where we study non-weakly compact sets with the fixed point property. Our approach brings a positive answer to a recent question raised by Gallagher et al. in (J Math Anal Appl 431(1):471–481, 2015). On the other side, we introduce a new metric structure closely related to the notion of relative uniform normal structure, for which we show that it implies the fixed point property under adequate conditions. This will provide some stability fixed point results in the context of hyperconvex metric spaces. As a particular case, we will prove that the set M=[−1,1]NM=[−1,1]N has the fixed point property for d-nonexpansive mappings where d(⋅,⋅)d(⋅,⋅) is a metric verifying certain restrictions. Applications to some Nakano-type norms are also given. |
Cita | Espínola García, R., Japón Pineda, M.d.l.Á. y Souza, D. (2021). New examples of subsets of c with the FPP and stability of the FPP in hyperconvex spaces. Journal of Fixed Point Theory and Applications, 23 (3), 45-1-45-19. |
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