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Global Invertibility of Expanding Maps

Jorge E. Hernández and M. Zuhair Nashed
Proceedings of the American Mathematical Society
Vol. 116, No. 1 (Sep., 1992), pp. 285-291
DOI: 10.2307/2159325
Stable URL: http://www.jstor.org/stable/2159325
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Global Invertibility of Expanding Maps
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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 α-expanding Fréchet differentiable map in Banach space under the assumption that the logarithmic norm of the derivative is negative.

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