Illinois Journal of Mathematics

On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets

Mohammed Bachir

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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.

Note

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.

Article information

Source
Illinois J. Math., Volume 61, Number 1-2 (2017), 1-24.

Dates
Received: 14 July 2016
Revised: 2 September 2017
First available in Project Euclid: 3 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1520046206

Digital Object Identifier
doi:10.1215/ijm/1520046206

Mathematical Reviews number (MathSciNet)
MR3770833

Zentralblatt MATH identifier
1395.46005

Subjects
Primary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10] 46B20: Geometry and structure of normed linear spaces 49J50: Fréchet and Gateaux differentiability [See also 46G05, 58C20]

Citation

Bachir, Mohammed. On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets. Illinois J. Math. 61 (2017), no. 1-2, 1--24. doi:10.1215/ijm/1520046206. https://projecteuclid.org/euclid.ijm/1520046206


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Corrections

  • Reprinted with corrections: Mohammed Bachir. On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets. Illinois Journal of Mathematics, Volume 62:1–4, 2018, pp. 1-24.