A generalization of the inverse mapping theorem in infinite dimensions

Sajjad Lakzian

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arXiv · 2604.10002

A generalization of the inverse mapping theorem in infinite dimensions

Sajjad Lakzian

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Abstract

We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property ${\sf A}$) replace the key $\mathsf{C}^1$ condition. We also obtain inverse mapping theorems that can be applied to non-smooth maps. Also as a by-product of the generalized inverse mapping theorem, we prove generalizations of the implicit function theorem and existence and uniqueness theorem of abstract PDE systems as well.

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Sajjad Lakzian. 2026-04-11. A generalization of the inverse mapping theorem in infinite dimensions. https://arxiv.org/abs/2604.10002

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