Talk:Banach fixed-point theorem

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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]