Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 62, Number 1-4 (2018), 1-24.
On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets
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.
Due to computer-generated errors that were introduced in the typesetting stage, this article, which originally appeared in the Illinois Journal of Mathematics (Volume 61:1–2, Spring and Summer 2017), is being reprinted in its entirety. The publisher apologizes for any inconvenience to readers.
Illinois J. Math., Volume 62, Number 1-4 (2018), 1-24.
Received: 14 July 2016
Revised: 2 September 2017
First available in Project Euclid: 13 March 2019
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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]
Bachir, Mohammed. On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets. Illinois J. Math. 62 (2018), no. 1-4, 1--24. doi:10.1215/ijm/1552442654. https://projecteuclid.org/euclid.ijm/1552442654