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- W2981428389 abstract "In this paper we show the following result: if C is an n-dimensional 0-symmetric convex compact set, $f:Crightarrow[0,1)$ is concave, and $g:[0,1)rightarrow[0,1)$ is not identically zero, convex, with g(0)=0, then [ frac{1}{|C|}int_C g(f(x))dx leq frac12 int_{-1}^1g(f(0)(1+t))dt, ] where |C| denotes the volume of C. If g? is strictly convex, equality holds if and only if f is affine, C is a generalized symmetric cylinder and f becomes 0 at one of the basis of C. We exploit this inequality to answer a question of Francisco Santos on estimating the volume of a convex set by means of the volume of a central section of it. Second, we also derive a corresponding estimate for log-concave functions." @default.
- W2981428389 created "2019-11-01" @default.
- W2981428389 creator A5059379235 @default.
- W2981428389 date "2019-08-18" @default.
- W2981428389 modified "2023-09-27" @default.
- W2981428389 title "On a generalization of the Hermite-Hadamard inequality and applications in convex geometry" @default.
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