The extrema of $q$- and dual $q$-quermassintegrals for the asymmetric $L_p$-difference bodies

Wang and Ma introduced the notion of asymmetric $L_p$-difference bodies. They further gave the extrema of volumes for the asymmetric $L_p$-difference body and its polar. Thereafter, Shi and Wang obtained their versions of quermassintegrals and dual quermassintegrals. In this paper, we determine the extrema of the $q$-quermassintegrals and dual $q$-quermassintegrals for the asymmetric $L_p$-difference bodies.