An inverse function theorem converse

被引：0

作者：

Lawson, Jimmie ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 486卷 / 02期

关键词：

Inverse function theorem; Lipschitz map; Banach space; Chain rule;

D O I：

10.1016/j.jmaa.2020.123913

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：6

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