Abstract
Abstract In the paper, our main aim is to generalize the dual affine quermassintegrals to the Orlicz space. Under the framework of Orlicz dual BrunnâMinkowski theory, we introduce a new affine geometric quantity by calculating the first-order variation of the dual affine quermassintegrals, and call it the Orlicz dual affine quermassintegral. The fundamental notions and conclusions of the dual affine quermassintegrals and the Minkoswki and BrunnâMinkowski inequalities for them are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions. The new OrliczâMinkowski and OrliczâBrunnâMinkowski inequalities in a special case yield the Orlicz dual Minkowski inequality and Orlicz dual BrunnâMinkowski inequality, which also imply the L p {L_{p}} -dual Minkowski inequality and BrunnâMinkowski inequality for the dual affine quermassintegrals.
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