L -Functions and Their Inverses
John S. Maybee, Gerry M. Wiener · SIAM Journal on Algebraic and Discrete Methods · 1987
Using concepts from qualitative matrix theory, we introduce a class of nonlinear mappings from $\mathbb{R}^n \to \mathbb{R}^n $ called L-functions. These generalize the L-matrices in much the same way that M-functions generalize M-matrices. We prove some global inverse function theorems for L-functions on several different types of domains without assuming that such functions are differentiable. Thus we do not make use of the Jacobian matrix. We also obtain interesting qualitative relations which must hold between an L-function and its inverse. Finally we prove a global implicit function theorem for L-functions, again without assuming differentiability.