Least fixed point

The function f(x) = x2 − 4 has two fixed points, shown as the intersection with the blue line; its least one is at 1/2 − √17/2.

In order theory, a branch of mathematics, the least fixed point (lfp or LFP, sometimes also smallest fixed point) of a function from a partially ordered set ("poset" for short) to itself is the fixed point which is less than each other fixed point, according to the order of the poset. A function need not have a least fixed point, but if it does then the least fixed point is unique.