A generalization of the inverse mapping theorem in infinite dimensions

We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property $\mathsf{A}$) 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.