Talk:Banach fixed-point theorem

Mathematics B‑class High‑priority

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Lipschitz constant

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)[reply]

Contractive Mapping Theorem

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[reply]

With what additional condition? Compactness? Algebraist 12:49, 24 September 2008 (UTC)[reply]

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)R.[reply]

Proofs are inappropriate for Wikipedia

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)[reply]

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 is 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, 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 most valuable quick reference, even if it is only available, and of interest, to the mathematically educated people, that is 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)[reply]