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On the inner and outer norms of sublinear mappings

Aragón Artacho, Francisco J. and Dontchev, Asen L. (2007) On the inner and outer norms of sublinear mappings. Set-Valued Analysis, 15 (1). pp. 61-65. ISSN 0927-6947

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    Abstract

    In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with dom F = X, is finite only if F is single-valued. This implies in particular that for a sublinear multivalued mapping the inner and the outer norms cannot be finite simultaneously.

    Item Type: Article
    Subjects: 47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
    Faculty: UNSPECIFIED
    Depositing User: Dr. Francisco Javier Aragón Artacho
    Date Deposited: 06 Sep 2011 15:44
    Last Modified: 13 Sep 2011 15:16
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/918

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