A Generalization of the Fujisawa–Kuh Global Inversion Theorem
نویسندگان
چکیده
We discuss the problem of global invertibility of nonlinear maps defined on the finite dimensional Euclidean space via differential tests. We provide a generalization of the Fujisawa-Kuh global inversion theorem and introduce a generalized ratio condition which detects when the pre-image of a certain class of linear manifolds is non-empty and connected. In particular, we provide conditions that also detect global injectivity.
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