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Remarks on “some fixed point theorems for s-convex subsets in p-normed spaces”

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Abstract

We explain why a recent proof of Schauder’s conjecture is not correct. A counterexample to a cited intermediate lemma is given.

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Notes

  1. A first proof was given by Robert Cauty [2,3,4]. A “very short outline of this extremely technical proof" can be found in [11, Sect. 5].

  2. The notion of p-normed spaces can be found in [12, p.1738].

  3. See Definition 2.2.

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Acknowledgements

I am deeply grateful to the referees for their review and valuable feedback, which significantly improved the exposition of this text. Their careful reading and constructive suggestions have been instrumental in enhancing the quality of this work.

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  1. Université Paris 1 Panthéon-Sorbonne, UMR 8074, Centre d’Economie de la Sorbonne, Paris, France

    Lu Yu

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  1. Lu Yu
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Yu, L. Remarks on “some fixed point theorems for s-convex subsets in p-normed spaces”. J Anal 32, 1139–1143 (2024). https://doi.org/10.1007/s41478-023-00678-0

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