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MINIMAX AND MAXIMIN REPRESENTATIONS OF POSITIVELY HOMOGENEOUS FUNCTIONS THROUGH LINEAR FUNCTIONS

Abstract

For functions, which belong to different (continuous, Lipschitz, difference-sublinear, piecewise-linear) subspaces of the space of positively homogeneous functions, we prove the existence and establish the characteristic properties of a two-index family of linear functions which provides simultaneously both minimax and maximin representations of such functions.
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ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)