On some generalizations of Hadamard's inversion theorem beyond differentiability

Abstract

A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the existence of global Lipschitz continuous inverse by translating its assumptions of metric nature in terms of nonsmooth analysis constructions. This exploration focuses on continuous, but possibly not locally Lipschitz mappings, acting in finite-dimensional Euclidean spaces. As a result, sufficient conditions for global invertibility are formulated by means of strict estimators, ∗ -difference of convex compacta and regular/basic coderivatives. These conditions qualify the global inverse as a Lipschitz continuous mapping and provide quantitative estimates of its Lipschitz constant in terms of the above constructions.