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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)
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)R
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.
Wikipedia is not a textbook, so proofs are generally not appropriate in articles. Even when a proof is of special interest in itself, e.g. for historical reasons (which is not the case here), it suffices to outline the main ideas and provide a reference for the deails. So I propose that the "Proof" section be removed. There may be a place for it in Wikibooks, hopefully. All the best, -- Jorge Stolfi ( talk) 02:03, 30 December 2009 (UTC)
Since you put it as a general principle, let me take the opportunity for some general remarks too. An encyclopedia like wikipedia provides information at various levels, and this is agreed as one main reason of its success. As a consequence, we must live with the idea that wikipedia should also contain some information which is of very high interest to very few users. The alternative entails a strong risk of devolving quickly into a flat list of trivialities. Here the issue of respecting the needs of a minority is not just in order to aknowledge an instance of democracy: if we remove the specialized material, most of the specialized contributors will eventually leave, and the general, non-specialized information will suffer as well. In particular, in many cases, a sketch of a proof is a very valuable quick reference, even if it is only available, and of interest, to the mathematically educated people. That is, to a small minority: though vital to wikipedia. In the present particular case, however, I agree that the proof is quite a bit longer than needed, and the main issues of the result may be stated a bit better. -- pm a ( talk) 11:29, 30 December 2009 (UTC)
I disagree that proofs should be completely removed from an article with reference to a general guideline as opposed to specific reference to the article in question. Although an article on compact spaces should not contain a proof of the Gelfand-Naimark theorem (for instance), the article on the Gelfand-Naimark theorem should contain such a proof. In fact, an article on "theorem X" should contain a proof of "theorem X"; after all, this is an encyclopedia and we should strive to include the most important details about "theorem X". What is more important than its hypothesis, implications within mathematics, and its proof? Applying general guidelines such as "mathematics articles should not contain proofs" should be done with care, especially if the article in question is about a proof. -- PS T 13:20, 3 January 2010 (UTC)
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)
...is not what this journal is called! 80.47.199.50 ( talk) 12:14, 9 January 2016 (UTC)
The comment(s) below were originally left at Talk:Banach fixed-point theorem/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
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Cronholm144 20:44, 21 May 2007 (UTC)
I am new in Wikipedia, but I think it is possible to improve this article. For example, there are a lot of applications of the Banach fixed point. I want to do this list. -- Incredulo ( talk) 00:27, 24 June 2008 (UTC)Incredulo |
Substituted at 18:09, 17 July 2016 (UTC)