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Gardner and Giannopoulos defined the p -cross-section body CpK ( p > −1) of convex body K in Euclidean space En . In this paper, we obtain inequalities for dual quermassintegrals of the p -cross-section body CpK . Further, two monotonic inequalities concerning the CpK are given.

Inequalities for dual quermassintegrals of the $p$-cross-section bodies