Support cones and convexity of sets in

Authors:
Robert Huotari and Junning Shi

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

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Abstract | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0002-9939-96-03347-3

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

Article copyright:
© Copyright 1996
American Mathematical Society