Talk:Schauder fixed-point theorem: Difference between revisions

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Latest revision as of 16:50, 16 April 2025

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Further updates on http://mathoverflow.net/questions/165853/is-schauders-conjecture-resolved also suggest that Cauty established the proof of Schauder's conjecture in the paper "[https://www.degruyter.com/abstract/j/crll.ahead-of-print/crelle-2014-0134/crelle-2014-0134.xml Un theoreme de Lefschetz-Hopf pour les fonctions a iterees compactes]", published online in 2015. --[[User:Saung Tadashi|Saung Tadashi]] ([[User talk:Saung Tadashi|talk]]) 17:32, 8 November 2016 (UTC)

:the link to Cauty's article is dead. [[User:Logicdavid|Logicdavid]] ([[User talk:Logicdavid|talk]]) 16:46, 16 April 2025 (UTC)

:Moreover, the article is not referenced at all in the wikipedia article, is it? [[User:Logicdavid|Logicdavid]] ([[User talk:Logicdavid|talk]]) 16:50, 16 April 2025 (UTC)

==Singbal generalization ==

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== References missing in text ==

The article states

The article states ``[Schauder's Fixed Point Theorem] asserts that if is a nonempty convex closed subset of a Hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of , then has a fixed point. That's not what is called Schauder's Fixed Point Theorem in most texts in the literature, namely because the latter usually concern Banach spaces. The theorem as stated here is moreover without citation. This is a significant problem, in my view. Where is this purported theorem from, exactly? Logicdavid (talk) 16:34, 16 April 2025 (UTC) [[User:Logicdavid|Logicdavid]] ([[User talk:Logicdavid|talk]]) 16:36, 16 April 2025 (UTC)

<blockquote>

[Schauder's Fixed Point Theorem] asserts that if C is a nonempty convex closed subset of a Hausdorff topological vector space and is f continuous mapping of C into itself such that is contained in a compact subset of C, then f has a fixed point.

</blockquote>

The article states ``[Schauder's Fixed Point Theorem] asserts that if is a nonempty convex closed subset of a Hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of , then has a fixed point. That's not what is called Schauder's Fixed Point Theorem in most texts in the literature, namely because the latter usually concern Banach spaces. The theorem as stated here is moreover without citation. This is a significant problem, in my view. Where is this purported theorem from, exactly? Logicdavid (talk) 16:34, 16 April 2025 (UTC) ''[[User:Logicdavid|Logicdavid]] ([[User talk:Logicdavid|talk]]) 16:36, 16 April 2025 (UTC)''

== A ghost Theorem ==

The article also coins the expression ``''Leray–Schauder theorem'' without telling us whatwhich theorem it might mean. Which theoremthis is it, where it can it be found, what does it state?states precisely. [[User:Logicdavid|Logicdavid]] ([[User talk:Logicdavid|talk]]) 16:39, 16 April 2025 (UTC)