2018/12/18 by Mohammed Bachir, Bachir, Mohammed
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.1812.07243
openalex publication_date 2018/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 .