FIND ME ON

GitHub

LinkedIn

Banach's Fixed Point

🌱

Theorem
StochasticControl

Let (X,d)(X,d) be a non-empty complete metric space with contraction map T:Xβ†’XT:X\to X. Then, TT admits a unique fixed point xβˆ—βˆˆXx^{*}\in X with T(xβˆ—)=xβˆ—T(x^{*})=x^{*}Furthermore, for any initial point x0∈Xx_{0}∈X the sequence defined by xn+1=T(xn)x_{n+1} = T(x_n) converges to the fixed point xβˆ—x^* as nβ†’βˆžn \to \infty.