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.

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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.