Fixed points of contractions approximating 1-Lipschitz maps

2019/03/13 by Maxime Zavidovique, Zavidovique, Maxime
Mathematics · Physics and Astronomy · Computer Science · #Fixed Point Theorems Analysis #Advanced Differential Geometry Research #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1903.05389

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, f_λ. We study the convergence of the fixed points of those contractions as they converge to f.

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