Open Access
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.

Version Information

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

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