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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Extremal Minkowski additive selections of compact convex sets
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by Rade T. Živaljević PDF
Proc. Amer. Math. Soc. 105 (1989), 697-700 Request permission

Abstract:

A function $f:{\mathcal {K}^n} \to {R^n}$, defined on the set of all compact convex sets in ${R^n}$, is a Minkowski additive selection, provided $f(K + L) = f(K) + f(L)$ and $f(K) \in K$ for all $K,L \in {\mathcal {K}^n}$. The paper deals with selections which are extremal in some sense, in particular we characterize the set of all Minkowski additive selections which have the property $f(K) \in {\text {ext}}(K)$ for all $K \in {\mathcal {K}^n}$, where ${\text {ext}}(K)$ is the set of all extreme points of $K$.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 697-700
  • MSC: Primary 52A20
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0937855-3
  • MathSciNet review: 937855