Fixed point property for nonexpansive
mappings and nonexpansive semigroups on
the unit disk
LUIS BENÍTEZ-BABILONIA*
Universidad de Antioquia, Instituto de Matemáticas, Medellín, Colombia.
Abstract. For closed convex subsets D of a Banach spaces, in 2009, Tomonari
Suzuki [11] proved that the fixed point property (FPP) for nonexpansive
mappings and the FPP for nonexpansive semigroups are equivalent. In this
paper some relations between the aforementioned properties for mappings
and semigroups defined on D, a closed convex subset of the hyperbolic metric
space (, ρ), are studied. This work arises as a generalization to the space
(
, ρ) of the study made by Suzuki.
Keywords: ρ-nonexpansive mappings, fixed point property, semigroups.
MSC2010: 47H09, 47H10, 30C99.
Propiedad del punto fijo para funciones y semigrupos
no expansivos en el disco unidad
Resumen. Para subconjuntos D cerrados y convexos de espacios de Banach,
Tomonari Suzuki [11] demostró en 2009 que la propiedad del punto fijo (PPF)
para funciones no expansivas y la PPF para semigrupos de funciones no expansivas
son equivalentes. En este trabajo se estudian algunas relaciones entre
dichas propiedades, cuando D es un subconjunto del espacio mético (, ρ).
Este trabajo surge como una generalización al espacio (
, ρ) de los resultados
de Suzuki.
Palabras clave: Funciones ρ-no expansivas, propiedad del punto fijo, semigrupos.
Texto Completo disponible en PDF
References
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*E-mail: lebenitez@cimat.mx.
Received: 11 December 2014, Accepted: 19 March 2015.
To cite this article: L. Benítez-Babilonia, Fixed point property for nonexpansive mappings and nonexpansive
semigroups on the unit disk, Rev. Integr. Temas Mat. 33 (2015), no. 1, 41-50.