Talk:Fixed-point theorem

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This page needs some organizing. As it stands, it may be a bit confusing. This is especially true because, in many contexts, a particular fixed point theorem is called the fixed point theorem. I noticed the diagonal lemma was not even connected with this page despite being called "fixed point theorem" in its Wikipedia page and "fixed point lemma" in my class and readings. We could start with a general discussion of the theorems at the top and then fork off into the separate theorems below. Teply (talk) 20:01, 10 December 2007 (UTC)Reply

It is custommary to write "fixed-point theorem", not "fixed point theorem". This is so because "fixed point theorem" might be read as "a fixed theorem about points". I suggest that there should be a redirection from fixed point theorem to fixed-point theorem, not vice versa. Frege (talk) 09:57, 16 January 2009 (UTC)Reply

It would be useful to have a couple of paragraphs outlining (and linking to) the many applications fixed-point theorems are. Brouwer's is necessary in many proofs related to noncooperative game theory, and Kakutani's involved in one of the versions of the General equilibrium model. My intuition tells me FPTs find applications in dynamic systems as well (a fixed point of a transition map is an equilibrium, ain't?) but this really should be written by a mathematician, preferably someone more from the side of teaching than research. --200.20.164.2 (talk) 18:47, 23 March 2010 (UTC)Reply