A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.
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added Wikipedia link (both as a useful link and also as the attribution where the tag-excerpt was taken from; AFAIK it is required CC BY-SA)
Martin Sleziak
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