Talk:Banach fixed-point theorem

message: The smallest such value of q is sometimes called the Lipschitz constant.
Any such q is a Lipschitz constant. There isn't the Lipschitz constant. 84.191.234.177 (talk) 20:09, 26 June 2008 (UTC)
thread_title:  Lipschitz constant 

message: Maybe a little note about Edelstein's contractive mapping theorem, a generalized version of the Contraction mapping theorem, which sets Lipschitz constant to be equal to 1 but makes the inequality strict should be added? 202.36.179.66 (talk) 02:06, 24 September 2008 (UTC)
replies: text: With what additional condition? Compactness? Algebraist 12:49, 24 September 2008 (UTC)
replies: text: Yep, compactness is the extra condition required to make the result go through. It was proved by M.Edelstein in the 60s and a constructive version of it was proved by D.Bridges in the 90s. The constructive formulation is, as one would expect, not nearly as general. Constructively, the proof for the existence of the fixed points is proved for all bounded euclidean spaces but the convergence of the iterates is only proven for up to 2 dimensions.121.73.122.128 (talk) 10:09, 26 September 2008 (UTC)
thread_title:  Contractive Mapping Theorem 

message: Proofs are not inappropriate for Wikipedia. However, the proof presented here is unnecessarily long and I think it was made that way so someone could plug their silly new proof. Someone with time on their hands should cut out the extra garbage. Sincerely, Zach.
:: Hear, hear.80.47.199.50 (talk) 12:17, 9 January 2016 (UTC)
replies: text:  Did my best.Student298 (talk) 21:38, 16 November 2018 (UTC)

text: I believe that we mostly agree.  I have nothing against specialized material per se, and indeed I believe that there is no such thing as a topic that is "too specialized" for Wikipedia.  I also believe that there are mny cases where a sketch of a proof does no harm.  However, I also believe that each article must be organized so that its is most convenient to read for most readers; and I do not believe that readers will be interested in proofs. These are useful only for two things: in books and journals, to prove to other skeptical fellow mathematicians that a claim is true; and in textbooks, to teach students to "think mathematically".  The former use is not applicable here since Wikipedia does not accept original research. (And, by the way, a proof specifically written for Wikipedia is uncomfortably close to being original research itself.)  As for the second use, Wikipedia is not (and should not be) a substitute for textbooks; and students already have plenty of proofs in their textbooks and classes. So, for most Wikipedia readers, proofs will be just useless clutter standing in the way of the facts. Look at articles on other sciences: there you will find lots of factual statements but hardly a hint of the detailed experiments and statistical analyses that were used to prove them.  Except for experiments of great historical value, the reader is expected to look for such details in the cited sources.  Why should math articles be different?However, I will not fight on this point; I only ask you to please consider whether the article gains or loses by including a proof of the theorem. All the best, --Jorge Stolfi (talk) 18:44, 30 December 2009 (UTC)
replies: text:  Proofs are not simply meant to validate claims like statements of p values and statistical methods. Proofs are different beasts that communicate additional information about the results. A p value in a journal does not aid the reader in understanding; however, a proof does. Likewise, it is not unprecedented for encyclopedia articles to describe how experiments are performed (e.g., the oil drop experiment). In the cases where a proof is destroying the readability of an article, it can be put inside a collapsible box. See Bernoulli's principle#Derivations_of_Bernoulli_equation for an example. —TedPavlic (talk/contrib/@) 22:25, 30 December 2009 (UTC)
thread_title:  Proofs are inappropriate for Wikipedia 

message: The contraction mapping theorem can be used to prove the existence and uniqueness of a solution to a differential equation. Can it be used for a stochastic differential equation?  Jackzhp (talk) 18:46, 11 July 2010 (UTC)
thread_title: Applications

message: ...is not what this journal is called!80.47.199.50 (talk) 12:14, 9 January 2016 (UTC)
thread_title:  Journal of Fixed Point Theory and its Application 

message: Substituted at 18:09, 17 July 2016 (UTC)
thread_title: Assessment comment