OAI/Analysis/Nonexpansive/Model.lean

GitHub source file

3 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.ReflexiveFixedPoints.CanonicallyReflexive line 14

    Source documentation

    Surjectivity of the canonical map into the continuous bidual.

    Also declared: ComparatorChallenges/ReflexiveFixedPoints.lean:14 (same declaration text).

    def CanonicallyReflexive : Prop :=
    …
  2. def OAI.ReflexiveFixedPoints.NonexpansiveOn line 20

    Source documentation

    Nonexpansiveness is measured in the original ambient norm.

    def NonexpansiveOn (C : Set X) (F : C → C) : Prop :=
    …
  3. def OAI.ReflexiveFixedPoints.HasNonexpansiveFixedPointProperty line 25

    Source documentation

    Every nonexpansive selfmap of every nonempty closed bounded convex set has a fixed point, in the norm already carried by X.

    def HasNonexpansiveFixedPointProperty (X : Type u)
        [NormedAddCommGroup X] [NormedSpace ℝ X] : Prop :=
    …