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Inverse and Implicit Function Theorems for Nonsmooth Maps in Banach Spaces

✍ Scribed by Zsolt Páles

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
273 KB
Volume
209
Category
Article
ISSN
0022-247X

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✦ Synopsis

We extend the classical inverse and implicit function theorems, the implicit function theorems of Lyusternik and Graves, and the results of Clarke and Pourciau to the situation when the given function is not smooth, but it has a convex strict prederivative whose measure of noncompactness is smaller than its measure of surjectivity. The proof of the main results requires Banach's open mapping theorem, Michael's selection theorem, Ekeland's variational principle, and Kakutani's fixed point theorem.

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