Open AccessEstimates on the size of the domain of weak invertibility in a form of the inverse mapping theorem
Author(s) -
Maurice Hasson,
Michael Tabor
Publication year - 2004
Publication title -
publikacija elektrotehnickog fakulteta - serija matematika
Language(s) - English
Resource type - Journals
eISSN - 2406-0852
pISSN - 0353-8893
DOI - 10.2298/petf0415097h
Subject(s) - bounded function , bounded inverse theorem , inverse , mathematics , domain (mathematical analysis) , isomorphism (crystallography) , derivative (finance) , stability (learning theory) , space (punctuation) , constant (computer programming) , pure mathematics , normed vector space , discrete mathematics , combinatorics , mathematical analysis , bounded operator , computer science , geometry , crystallography , chemistry , machine learning , financial economics , crystal structure , programming language , economics , operating system
Let be a mapping of a normed space E to itself. Let the derivative D at be a bounded isomorphism on E with bounded inverse D-1. Assume in addition, that there exist constants C, r, α > 0 such that for . We show that f(a + h) ≠ f(a) whenever . In addition certain stability results of the nonlinear mapping f are established.
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