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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Support cones and convexity of sets in ${\mathbb {R}}^n$
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by Robert Huotari and Junning Shi
Proc. Amer. Math. Soc. 124 (1996), 2405-2414
DOI: https://doi.org/10.1090/S0002-9939-96-03347-3

Abstract:

We discuss several metric characterizations of convexity of sets in non-smooth finite-dimensional Banach spaces. We describe a setting in which convexity is equivalent to the rotation-invariance of various properties, including almost convexity, radial continuity of the metric projection, and Chebyshevity. One of the tools used is a generalization of norm-smoothness which involves support cones of the unit ball.
References
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Bibliographic Information
  • Robert Huotari
  • Affiliation: Department of Mathematics, Idaho State University, Pocatello, Idaho 83209
  • Address at time of publication: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322-3900
  • Email: huotari@isu.edu
  • Junning Shi
  • Affiliation: Permanent address  : Allianz Insurance Company, 3400 Riverside Dr., Suite 300, Burbank, California 91505
  • Received by editor(s): April 20, 1994
  • Received by editor(s) in revised form: February 10, 1995
  • Communicated by: J. Marshall Ash
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 2405-2414
  • MSC (1991): Primary 41A65; Secondary 41A62
  • DOI: https://doi.org/10.1090/S0002-9939-96-03347-3
  • MathSciNet review: 1327019