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Exact Formulae for Regularity Estimates

Ioffe, Alexander and Sekiguchi, Y. (2006) Exact Formulae for Regularity Estimates. [Preprint]

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    Abstract

    In the classical calculus a continuously Fr´echet differentiable mapping F from a Banach space X into another Banach space Y is called regular at x if F0(x), the derivative of F at x, maps X onto Y . According to the Lusternik–Gravestheorem this implies that the images of small balls around x cover balls centered at x whose ridii are proportional to the radii of the corresponding balls in X. Moreover, it turns out that the same is true for all y near x and a common coefficient of proportionality can be chosen for all y of a neighborhood of x. These are among the most fundamental facts of the classical calculus which are behind such results as the inverse and the implicit function theorem...

    Item Type: Preprint
    Additional Information: pubdom TRUE
    Subjects: 46-xx Functional analysis > 46Txx Nonlinear functional analysis
    47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 18 Jan 2006
    Last Modified: 21 Apr 2010 11:14
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/314

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