Source: wikibot/fixed-point-theorem
= Fixed-point theorem
{wiki=Fixed-point_theorem}
A fixed-point theorem is a fundamental result in various branches of mathematics, particularly in analysis and topology, that asserts the existence of fixed points under certain conditions. A fixed point of a function is a point that is mapped to itself by the function. Formally, if \\( f: X \\rightarrow X \\) is a function on a set \\( X \\), then a point \\( x \\in X \\) is a fixed point if \\( f(x) = x \\).