Talk:Contraction mapping

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Mathematics rating:	Stub Class	Mid Priority	Field: Analysis
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 20:52, 21 May 2007 (UTC)

In response to the question: "to anon: what's the anomaly?" on my last edit:

In the first section, 'contractions' and 'non-expansive maps' are defined. Contractions are maps that are Lipschitz continuous with Lipschitz constant <1. Non-expansive maps have Lipschitz constant ≤ 1.

In the operator theory section, a 'contraction' is a linear operator of norm ≤ 1. Thus a contraction is a non-expansive linear operator. Thus in operator theory, contraction means something very different than in the context of the first section. For example, the identity map is a contraction operator but not a contraction mapping, following these definitions.

128.135.100.161 01:20, 3 March 2007 (UTC)

well, if the issue is < 1 and ≤ 1...ok, there is a difference there. Mct mht 18:40, 3 March 2007 (UTC)

So to say 'as a special case of the above definition' is a bit misleading... I will trust your judgment on the best way to change the wording, but no change at all does not seem very considerate to readers. 128.135.100.161 20:28, 8 March 2007 (UTC)

yes, you're right. i disagreed with your previous changes because to emphasize this slight difference seemed somewhat misleading as well. but maybe the difference is not so slight. the contraction mapping theorem requires < 1 and would not apply to the operator case. i am going to revert article to your last version. Mct mht 22:12, 8 March 2007 (UTC)

[edit] "A contraction mapping has at most one fixed point."

"A contraction mapping has at most one fixed point." Isn't this only true for non-expansive maps? Oops, never mind that. Arthena^(talk) 21:11, 21 January 2008 (UTC)