The quermassintegrals form of the polar duality of Brunn–Minkowski inequality was established by Firey. In 2016, Cifre and Nicolas gave the quermassintegrals form of the polar duality of Lₚ -Brunn–Minkowski inequality. In this paper, we extend Cifre and Nicolas’s result to q -quermassintegrals form. Further, as the applications of this result, we separately give the q -quermassintegrals form of the Lₚ -dual Brunn–Minkowski inequality and the extremums of q -quermassintegrals of the polar asymmetric Lₚ -difference bodies.
W. D. Wang (2025) studied this question.