Browder convergence theorem for averaged operators
= Browder convergence theorem for averaged operators
{c}
In finite-dimensional Euclidean space, iterating an <averaged operator> with a nonempty fixed-point set converges in norm to a fixed point from every start. The <averaged-operator inequality> proves boundedness and a vanishing residual; compactness produces a fixed cluster point and <Fejér monotonicity> turns subsequential convergence into convergence of the full sequence. A fixed point must exist.