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Global invertibility of expanding maps

Authors: Jorge E. Hernández and M. Zuhair Nashed
Journal: Proc. Amer. Math. Soc. 116 (1992), 285-291
MSC: Primary 58C15; Secondary 47H15
MathSciNet review: 1110543
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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 $ \alpha $-expanding Fréchet differentiable map in Banach space under the assumption that the logarithmic norm of the derivative is negative.

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Keywords: Global inverse mapping theorems, $ \alpha $-expanding maps, logarithmic norm, interior mapping theorem, Fréchet derivative
Article copyright: © Copyright 1992 American Mathematical Society

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