Browsing by Autor "Nelson Merentes"

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    Strongly convex set-valued maps
    (Springer Science+Business Media, 2013) Hugo Leiva; Nelson Merentes; Kazimierz Nikodem; José L. Sánchez
    We introduce the notion of strongly $$t$$ -convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps, as well as a Kuhn-type result are obtained. A representation of strongly $$t$$ -convex set-valued maps in inner product spaces and a characterization of inner product spaces involving this representation is given. Finally, a connection between strongly convex set-valued maps and strongly convex sets is presented.