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    Notes on extended real- and set-valued functions

    Date
    2012
    Author
    Hamel, AH
    Schrage, C
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    Abstract
    An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving −∞ and/or +∞, so-called residuations. Based on this, definitions and results for directional derivatives, subdifferentials and Legendre--Fenchel conjugates for extended real-valued functions are given which admit to include the proper as well as the improper case. For set-valued functions, scalar representation theorems and a new conjugation theory are established. The common denominator is that the appropriate image spaces for set-valued functions share fundamental structures with the extended real numbers: They are order complete, residuated monoids with a multiplication by non-negative real numbers.
    URI
    http://hdl.handle.net/10863/628
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    • Articles - Economics and Management

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