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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2159325
Page Count: 7
You can always find the topics here!Topics: Banach space, Mathematical theorems, Homeomorphism, Mathematical problems, Invertibility, Functional analysis, Hilbert spaces, Linear transformations, Mathematical constants
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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.
Proceedings of the American Mathematical Society © 1992 American Mathematical Society