Guillermo Sierra
Abstract
The purpose of this note is to give a proof, hopefully new, of the inverse function theorem as an application of the local existence theorem for differential equations. If Ω is an open subset of a Banach space E and T: Ω → E is of class C 1 , then T is locally bounded and satisfies a Lipschitz condition at every point.
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The purpose of this note is to give a proof, hopefully new, of the inverse function theorem as an application of the local existence theorem for differential equations. If Ω is an open subset of a Banach space E and T: Ω → E is of class C 1 , then T is locally bounded and satisfies a Lipschitz condition at every point.
Key concepts: Mathematics, Bounded inverse theorem, Inverse function theorem, Lipschitz continuity, Bounded function, Banach space, Picard–Lindelöf theorem, Class (philosophy)