Recent zbMATH articles in MSC 46Thttps://www.zbmath.org/atom/cc/46T2021-04-16T16:22:00+00:00WerkzeugAn inverse function theorem converse.https://www.zbmath.org/1456.460672021-04-16T16:22:00+00:00"Lawson, Jimmie"https://www.zbmath.org/authors/?q=ai:lawson.jimmie-dSummary: We establish the following converse of the well-known inverse function theorem. Let \(g : U \to V\) and \(f : V \to U\) be inverse homeomorphisms between open subsets of Banach spaces. If \(g\) is differentiable of class \(C^p\) and \(f\) is locally Lipschitz, then the Fréchet derivative of \(g\) at each point of \(U\) is invertible and \(f\) must be differentiable of class \(C^p\).