Functions with Positive Differences on Convex Cones
Author(s)
Niculescu, Constantin P.; Sra, Suvrit
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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,
$$f\left( x\right) +f\left( y\right) +f\left( z\right) +f\left( x+y+z\right) \ge f\left( x+y\right) +f\left( y+z\right) +f\left( z+x\right) +f(0),$$
f
x
+
f
y
+
f
z
+
f
x
+
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+
z
≥
f
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+
y
+
f
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f
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(
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.
Date issued
2023-08-19Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Institute for Data, Systems, and SocietyPublisher
Springer International Publishing
Citation
Results in Mathematics. 2023 Aug 19;78(6):217
Version: Author's final manuscript