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Support cones and convexity of sets in ${\mathbb {R}}^n$

Authors: Robert Huotari and Junning Shi
Journal: Proc. Amer. Math. Soc. 124 (1996), 2405-2414
MSC (1991): Primary 41A65; Secondary 41A62
MathSciNet review: 1327019
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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.

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Additional 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

Junning Shi
Affiliation: Permanent address : Allianz Insurance Company, 3400 Riverside Dr., Suite 300, Burbank, California 91505

Keywords: Metric projection, support cone, convexity
Received by editor(s): April 20, 1994
Received by editor(s) in revised form: February 10, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society