Geodesic
Jensen-type geometric shapes
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 27-33.

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We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary. It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.
Keywords: Shapes; Platonic shapes; sphere; ball; Jensen's inequality 
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Pasteczka, Paweł. Jensen-type geometric shapes. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 27-33. http://geodesic.mathdoc.fr/item/AUPCM_2020_19_a1/

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