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

Mohammed Bachir (1)

1 Equations d'evolution

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.

Keywords: Extreme points; Krein-Milman theorem; variational principle.; $\Phi$-convexity; exposed and $\Phi$-exposed points

Domains: Functional Analysis [math.FA]

Mohammed Bachir. On the Krein-Milman-Ky Fan theorem for convex compact metrizable sets.. Illinois Journal of Mathematics, 2018, 62 (1-4). ⟨hal-01576780⟩