Functional analysis·OpenAI Math·Result 328·Lean formalisation listed
Nonexpansive fixed points in reflexive Banach spaces
One of the 372 results in OpenAI's public mathematics catalogue, filed under functional analysis: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Fixed Points of Nonexpansive Maps in Reflexive Banach Spaces
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What OpenAI claims
Resolves Kirk's reflexive-space fixed-point problem: every nonexpansive selfmap of a nonempty closed bounded convex subset of a real reflexive Banach space has a fixed point. The result uses the original norm, without assuming uniform convexity. (Lean)
Paper
Fixed Points of Nonexpansive Maps in Reflexive Banach Spaces
Every nonexpansive selfmap of a nonempty closed bounded convex subset of a real reflexive Banach space has a fixed point. This resolves the reflexive-space fixed point problem for the given norm.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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