Geometria Tanszék Bolyai Intézet, TTI Kar, Szegedi Tudományegyetem

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• #### Vígh Viktor habilitál

On extensions of Jensen and Hermite-Hadamard inequalities

A Geometriai Tanszék örömmel teszi közzé, hogy

Bernardo González Merino
(University of Sevilla, Spanyolország)

a Kerékjártó Szeminárium keretében előadást tart

On extensions of Jensen and Hermite-Hadamard inequalities

címmel.

2019. május 23, csütörtök 12:30 óra,
Riesz terem (BO-107)

The original Hermite-Hadamard inequality (1881-1893) states that for any $f\colon\mathbb R\to\mathbb R$ concave function it holds that $\frac{f(a)+f(b)}{2} \leq \frac{1}{b-a}\int_a^bf(x)dx \leq f\left(\frac{a+b}{2}\right).$ In this talk we will present new extensions of this inequality in $\mathbb R^n$ replacing $f(x)$ by $f(x)^m$ for some $m\in\mathbb N$. As an application to these new inequalities we will obtain new Rogers-Shephard type inequalities. The latter inequality relates the volume of a convex set $K\subset\mathbb R^n$ with the volume of some of its sections and projections with respect to some linear subspaces; one of such is considered as a reverse Brunn-Minkowski inequality.