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Prove ReflexiveFixedPoints (openai/math family 328: Fixed points of nonexpansive maps in reflexive Banach…

Prove ReflexiveFixedPoints (openai/math family 328: Fixed points of nonexpansive maps in reflexive Banach…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 328 of the release, Fixed points of nonexpansive maps in reflexive Banach spaces…

The task

Context: this statement belongs to family 328 of the release, *Fixed points of nonexpansive maps in reflexive Banach spaces* (Functional analysis). The family as a whole: Resolves Kirk's reflexive-space fixed-point problem: every nonexpansive selfmap of a nonempty closed bounded convex subset of a real reflexive…

Part of raising-heart/openai-math.