EXTENSION OF THE BAUER'S MAXIMUM PRINCIPLE FOR COMPACT METRIZABLE SETS

Mohammed Bachir (1)

1 Equations d'evolution

Let X be a nonempty convex compact subset of some Haus-dorff locally convex topological vector space S. The well know Bauer's maximum principle stats that every convex upper semi-continuous function from X into R attains its maximum at some extremal point of X. We give some extensions of this result when X is assumed to be compact metrizable. We prove that the set of all convex upper semi-continuous functions attaining there maximum at exactly one extremal point of X is a G δ dense subset of the space of all convex upper semi-continuous functions equipped with a metric compatible with the uniform convergence .

Keywords: and phrases: Bauer's Maximum Principle; Variational Principle; Exposed and Extremal points; Convexity and Φ-convexity

Domains: Functional Analysis [math.FA]

Mohammed Bachir. EXTENSION OF THE BAUER'S MAXIMUM PRINCIPLE FOR COMPACT METRIZABLE SETS. 2018. ⟨hal-01956983⟩