Mann's iteration is the dynamical system defined for a continuous function f:[0, 1]->[0, 1], x_n = 1/n sum_(k = 0)^(n - 1) f(x_k) with x_0 element [0, 1]. It can also be written x_k = ((k - 1) x_(k - 1) + f(x_(k - 1)))/k. This iteration always converges to a fixed point of f.

map fixed point | Sharkovsky's theorem