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Support cones and convexity of sets in 
Author(s):
Robert
Huotari;
Junning
Shi
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2405-2414.
MSC (1991):
Primary 41A65;
Secondary 41A62
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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
Email:
huotari@isu.edu
Junning
Shi
Affiliation:
Allianz Insurance Company, 3400 Riverside Dr., Suite 300, Burbank, California 91505
DOI:
10.1090/S0002-9939-96-03347-3
PII:
S 0002-9939(96)03347-3
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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