On Discrete LOG-Brunn--Minkowski Type Inequalities

Cifre, María A. Hernández; Lucas, Eduardo

doi:10.1137/21m1451725

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Introduction and Main Results1

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2022

2023

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Cited by 2 publications

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“…More recently, different discrete analogues of the Brunn-Minkowski inequality have been obtained, including the case of its classical form (cf. (1.1)) for the cardinality [18,22,26], functional extensions of it [21,25,26,27,35] and versions for the lattice point enumerator G n (•) [21,23,26], which is given by G…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On Rogers–Shephard-type inequalities for the lattice point enumerator

Alonso–Gutiérrez

Lucas

Nicolás

2022

Commun. Contemp. Math.

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In this paper, we study various Rogers–Shephard-type inequalities for the lattice point enumerator [Formula: see text] on [Formula: see text]. In particular, for any non-empty convex bounded sets [Formula: see text], we show that [Formula: see text] and [Formula: see text] for [Formula: see text], [Formula: see text]. Additionally, a discrete counterpart to a classical result by Berwald for concave functions, from which other discrete Rogers–Shephard-type inequalities may be derived, is shown. Furthermore, we prove that these new discrete analogues for [Formula: see text] imply the corresponding results involving the Lebesgue measure.

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