Least fixed point

In mathematics, the least fixed point in order theory of a function is the fixed point which is less than or equal to all other fixed points, according to some partial order.

For example, the least fixed point of the real function

f(x) = x²

is x = 0 with the usual order on the real numbers. Many fixed-point theorems yield algorithms for locating the least fixed point. Least fixed points often have desirable properties that arbitrary fixed points do not.

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