Talk:Schauder fixed-point theorem: Difference between revisions

Revision as of 21:56, 22 February 2017

Revision as of 08:27, 3 December 2020

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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)

==Singbal generalization ==

Someone wrote:

<blockquote>B. V. Singbal proved the theorem for the more general case where '''K may be non-compact'''; the proof can be found in the appendix of Bonsall's book (see references).

</blockquote>

However, the appendix of Bonsall's book contains only this theorem

<blockquote>

'''Theorem.''' (Singbal).Let E be a locally convex Hausdorff l.t.s., K a non-empty closed convex subset of E, T a continuous mapping of K into '''a compact subset of K'''. Then T has a fixed point in K.

<blockquote>

Since x is a fixed point of T in K if and only if x is a fixed point in T(K), this theorem still uses the compactness of the set.

--[[User:Chyyr|Chyyr]] ([[User talk:Chyyr|talk]]) 08:27, 3 December 2020 (UTC)