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Browsing by Subject "Bernstein-Doetsch--type theorem"

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    Item type:Article, Access status: Open Access ,
    On strongly midconvex functions
    (2011) Azócar, A.; Giménez, J.; Nikodem, K.; Sánchez, J. L.
    In this paper we collect some properties of strongly midconvex functions. First, counterparts of the classical theorems of Bernstein-Doetsch, Ostrowski and Sierpiński are presented. A version of Rod é support theorem for strongly midconvex functions and a Kuhn-type result on the relation between strongly midconvex functions and strongly $t$-convex functions are obtained. Finally, a connection between strong midconvexity and generalized convexity in the sense of Beckenbach is established.