Publication:
On Rogers-Shephard type inequalities for thelattice point enumerator

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Date
2022-02-25
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Authors
Alonso Gutiérrez, David ; Lucas Marín, Eduardo ; Yepes Nicolás, Jesús
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Publisher
World Scientific Publishing
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Matemáticas
DOI
https://doi.org/10.1142/S0219199722500225
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info:eu-repo/semantics/article
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Abstract
Abstract. In this paper we study various Rogers-Shephard type inequalities for the lattice point enumerator Gn(·) on Rn. In particular, for any non-empty convex bounded sets K,L ⊂ Rn. 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 Gn(·) imply the corresponding results involving the Lebesgue measure.
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Rogers Shephard inequality , Lattice point enumerator , Berwald’s inequality , Projection section inequality
Citation
Communications in Contemporary MathematicsVol. 25, No. 08, 2250022 (2023)
URI
http://hdl.handle.net/10201/215141
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