TheIn [[functional analysis]], the '''Ryll-Nardzewski fixed point theorem''' states that if <math>E</math> is a [[normed vector space]] and <math>K</math> is nonempty [[convexity|convex]] subset of <math>E</math>, which is [[closed set|closed]] for the [[weak topology]], then every group of [[affine map|affine]] [[isometry|isometries]] of <math>K</math> has aat least one [[fixed point]].
