Work

An unbounded convex set with the fixed point property for nonexpansive mappings

Year: 2026

Type: preprint

Abstract: We construct an equivalent norm on $\mathbb{R}\oplus\ell_2$ and a nonempty closed convex unbounded subset having the fixed point property for nonexpansive self-mappings. The ambient renormed space has the fixed point property on bounded closed convex subsets. The main point is a geometric localization estimate at a distinguished point of the unbounded set; the fixed point conclusion then follows from the Kirk--Ray localization theorem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.14868

Authors: Japón, M., Laguna-Ricart, Javier

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Universidad de Murcia, European Regional Development Fund, Agencia Estatal de Investigación

Awards: G2146289210, G2573088050, G4025565791, G410571670, G451917667, G4907579104, G5967599077, G675437911, G8165088388

OpenAlex ID: W7221812830

Cites: 8

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Related to: 10