Functions with Positive Differences on Convex Cones
Name
25_2023_1987_ReferencePDF.pdf
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Author(s)
Niculescu, Constantin P.
Sra, Suvrit
Date Issued
August 19, 2023
Publisher
Springer International Publishing
Citation
Results in Mathematics. 2023 Aug 19;78(6):217
Version
Author's final manuscript
Abstract
Abstract
We analyze the role played by functions with positive differences defined on convex cones. In particular, we study functions that satisfy linear functional inequalities that extend the three-variable Hornich-Hlawka functional inequality,
$$f\left( x\right) +f\left( y\right) +f\left( z\right) +f\left( x+y+z\right) \ge f\left( x+y\right) +f\left( y+z\right) +f\left( z+x\right) +f(0),$$
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especially to the case of n variables. Beyond the classical setting, we present extensions to the case of positive operators.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00025-023-01987-3
