Ryll-Nardzewski fixed-point theorem: Difference between revisions

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In [[functional analysis]], the '''Ryll-Nardzewski fixed point theorem''' states that if <math>E</math> is a [[normed vector space]] and <math>K</math> is a nonempty [[Convex set|convex]] subset of <math>E</math> which is [[compact space|compact]] under the [[weak topology]], then every [[group (mathematics)|group]] (or equivalently: every [[semigroup]]) of [[affine map|affine]] [[isometry|isometries]] of <math>K</math> has at least one fixed point. (Here, a ''fixed point'' of a set of maps is a point that is a [[fixed point]] for each of the set's members.)