Fixed points of contractions approximating 1-Lipschitz maps
Abstract
A 1-Lipschitz map f from a convex compact set to itself has fixed points. This consequence of Brouwer's or Schauder's fixed point theorem has more elementary proofs by approximating f by λ-contractions, fλ. We study the convergence of the fixed points of those contractions as they converge to f.
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