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arXiv · 2610.14868

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

M. Japón·Javier Laguna-Ricart
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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.

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M. Japón, Javier Laguna-Ricart. 2026-10-10. An unbounded convex set with the fixed point property for nonexpansive mappings. https://arxiv.org/abs/2610.14868

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