Global invertibility of expanding maps

Abstract

We prove a global inversion theorem in reflexive Banach spaces utilizing a recent generalization of the interior mapping theorem. As a corollary, we provide, under a mild approximation property, a positive answer to an open problem that was stated by Nirenberg. We also establish global invertibility of an α \alpha -expanding Fréchet differentiable map in Banach space under the assumption that the logarithmic norm of the derivative is negative.