An Inverse Function Theorem Converse

2018/12/09 by Lawson, Jimmie D.
#58C20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1812.03561

Abstract

We establish the following converse of the well-known inverse function theorem. Let g:U→ V and f:V→ U be inverse homeomorphisms between open subsets of Banach spaces. If g is differentiable of class C^p and f if locally Lipschitz, then the Fréchet derivative of g at each point of U is invertible and f must be differentiable of class C^p.

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