Talk:Common fixed point problem

I believe that this subject is notable due to:

• The significant amount of attention given to the problem during the period when it was unsolved, as evidenced by the sources
• The publication of articles and papers about the problem even decades after it was solved (the articles by Brown and McDowell, and the master's thesis by McCroskey)
• The continued relevance of Baxter permutations, which arose directly from research into this problem
• References to the work of Boyce and/or Huneke in recent research, e.g., "On distal flows and common fixed point theorems in Banach spaces" (https://doi.org/10.1016/j.jmaa.2022.126995), published in 2023, references the "Commuting functions with no common fixed point" paper
• Showing up on Math StackExchange and other sites from time to time (e.g., https://math.stackexchange.com/questions/4413605/continuous-function-on-the-unit-interval-with-commuting-compositions)

Citation needed

Regarding a citation for the statement "Huneke's paper is notable for its first-principles approach to the problem, not relying on any of the work done by earlier mathematicians." My source is Huneke's paper itself. It only has three references: two are to Boyce's dissertation and his Transactions paper, and the third is to Huneke's own dissertation. WillisBlackburn (talk) 17:20, 16 October 2024 (UTC)

Did you know nomination

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• Comment or view
• Article history

)

• ... that in 1967, two mathematicians published PhD dissertations independently disproving the same thirteen-year-old conjecture?

• Source: "The purpose of this paper is to answer Dyer's question in the negative by the construction of a pair of commuting functions which have no fixed point in common. [...] This paper is a condensation of the author's 1967 doctoral dissertation", from a paper by Boyce . "It has been conjectured that any two continuous functions f, g mapping the closed unit interval into itself which commute under composition [...] must have a common fixed point [...] Chapter 2 defines a pair of functions which show that the conjecture is false", from Huneke's 1967 PhD dissertation.

• Reviewed:
• Comment: If the reviewer doesn't have ProQuest access, I can provide a copy of Huneke's dissertation over email.

Created by WillisBlackburn (talk). Number of QPQs required: 0. Nominator has fewer than 5 past nominations.

jlwoodwa (talk) 19:15, 16 October 2024 (UTC).

• Starting review...
• Article is new enough and long enough
• Sources all appear to be WP:RS and for the most part, adequately cited with in-line citations. There are however two {{citation needed}} tags which need to be addressed.
• Earwig calls out a few phrases here and there but they all look like technical terms which can't be rephrased, so no problems there.
• Extra brownie points for taking an exceptionally technical article and writing a hook which will appeal to most readers. RoySmith (talk) 22:16, 13 November 2024 (UTC)

@Jlwoodwa: just want to make sure you saw this. RoySmith (talk) 01:18, 18 November 2024 (UTC)

@RoySmith: Thanks for the ping. I've removed the first statement tagged with {{citation needed}} (since WillisBlackburn said on the talk page that it turned out to be false), and added a citation for the other statement. jlwoodwa (talk) 01:58, 18 November 2024 (UTC)

Looking at this closer, I see that there's still some statements that need citations. I've added some more {{citation needed}} tags. My apologies for not picking up on this the first time. RoySmith (talk) 02:06, 18 November 2024 (UTC)

@Jlwoodwa: please see the above. RoySmith (talk) 14:21, 22 November 2024 (UTC)

Looks like the claim in the hook is sourced to the dissertations themselves, so there's no source actually saying they were independent, which sounds like a WP:SYNTH problem to me. theleekycauldron (talk • she/her) 11:16, 28 November 2024 (UTC)

Secondary sources agree that Boyce and Huneke came up with their solutions independently. For example, from the Brown article: "It seems appropriate that a question that independently occurred to more than one person should have been answered independently by two people." The McDowell article: "The Dyer/Shields/Dubins/Isbell conjecture (hereafter referred to as the common fixed-point conjecture) was independently settled in the negative by William M. Boyce [7] and Huneke [22] in 1967." The McCrosky dissertation: "Finally, in 1967, the unit interval was shown to not have the common fixed point property by two men working independently on their dissertations." And of course Huneke's published paper (separate from his disseration) says "Simultaneous to and independent of the author's preceding work, W. M. Boyce [1], [2] constructed essentially the same solution." WillisBlackburn (talk) 22:33, 28 November 2024 (UTC)

I'd like a copy of the Huneke disseration if you could provide it. Do you also have access to the Boyce dissertation? I only have the paper published in Transactions AMS. WillisBlackburn (talk) 21:23, 16 October 2024 (UTC)

Boyce is ProQuest 288201093. I appear to have access if you don't, but maybe the Wikipedia Library works for this?

Incidentally there is a [citation needed] tag and a few sentences at the ends of paragraphs that are not supported by footnotes that should be footnoted. Per WP:DYKCITE, every claim in a DYK article (not counting the summaries of later sourced material in the lead) must have a reference, not later than the end of its paragraph. —David Eppstein (talk) 07:41, 17 October 2024 (UTC)

I now have both. I'm going to have to change the statement that Huneke doesn't reference the prior researchers, because his dissertation does. The dissertation also includes a lot of narrative not in the paper he published in Transactions. WillisBlackburn (talk) 14:59, 18 October 2024 (UTC)