Strong Convergence of Cesaro Means of Firmly Nonexpansive Iterates
Iterates of a firmly nonexpansive operator converge weakly but not strongly, by Genel and Lindenstrauss. Whether their Cesaro means converge strongly was open. They need not: an explicit curve gives a counterexample.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Fixed point theory
- Posed by
- —
- Year posed
- 1975
- Years open
- 51y
- Solved
- 2026-05-25
- Model
- ChatGPT 5.5
- Vendor
- OpenAI
- Collaborators
- Heinz H. Bauschke, Tran Thanh Tung
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgement credits use of ChatGPT 5.5 as leading eventually to the realization of the explicit curve, which is the object the counterexample is built from.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2605.25491 - Cesaro means of firmly nonexpansive iterates need not converge strongly