An inverse function theorem converse

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Lawson, Jimmie¹ 

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

关键词: Inverse function theorem;    Lipschitz map;    Banach space;    Chain rule;   

DOI  :  10.1016/j.jmaa.2020.123913

来源: Elsevier

【 摘 要 】

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 is locally Lipschitz, then the Frechet derivative of g at each point of U is invertible and f must be differentiable of class C-P. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free