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Spring and Summer 2017 On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets
Mohammed Bachir
Illinois J. Math. 61(1-2): 1-24 (Spring and Summer 2017). DOI: 10.1215/ijm/1520046206

Abstract

We extend the extension by Ky Fan of the Krein–Milman theorem. The $\Phi $-extreme points of a $\Phi $-convex compact metrizable space are replaced by the $\Phi $-exposed points in the statement of Ky Fan theorem. Our main results are based on new variational principles which are of independent interest. Several applications will be given.

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Due to computer-generated errors that were introduced in the typesetting stage, this article has been reprinted in its entirety in the Illinois Journal of Mathematics (Volume 62:1–4, 2018, pp. 1-24). The publisher apologizes for any inconvenience to readers.

Citation

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Mohammed Bachir. "On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets." Illinois J. Math. 61 (1-2) 1 - 24, Spring and Summer 2017. https://doi.org/10.1215/ijm/1520046206

Information

Received: 14 July 2016; Revised: 2 September 2017; Published: Spring and Summer 2017
First available in Project Euclid: 3 March 2018

zbMATH: 1395.46005
MathSciNet: MR3770833
Digital Object Identifier: 10.1215/ijm/1520046206

Subjects:
Primary: 46B20, 46B22, 49J50

Rights: Copyright © 2017 University of Illinois at Urbana-Champaign

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Vol.61 • No. 1-2 • Spring and Summer 2017
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