The dual logarithmic Aleksandrov-Fenchel inequality. (English) Zbl 1462.52013
Summary: In this paper, we establish a dual logarithmic Aleksandrov Fenchel inequality involving logarithms by introducing new geometric measures and using the newly published \(L_p\)-dual Aleksandrov-Fenchel inequality. The dual logarithmic Aleksandrov-Fenchel inequality is also derived. This new dual logarithmic Aleksandrov-Fenchel type inequality in special cases yields \(L_p\)-dual logarithmic Minkowski’s inequality, the classical dual Aleksandrov-Fenchel inequality and related dual logarithmic Minkowski type inequalities.
MSC:
| 52A39 | Mixed volumes and related topics in convex geometry |
| 52A20 | Convex sets in \(n\) dimensions (including convex hypersurfaces) |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 52A40 | Inequalities and extremum problems involving convexity in convex geometry |
Keywords:
dual mixed volume; \(L_p\)-multiple dual mixed volume; Minkowski inequality; logarithmic Minkowski inequality; dual Aleksandrov-Fenchel inequality; \(L_p\)-dual Aleksandrov-Fenchel inequalityReferences:
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