The mixed L p -dual affine surface area for multiple star bodies

Associated with the notion of the mixed L p -affine surface area for multiple convex bodies for all real p ( p ≠ − n ) which was introduced by Ye, et al. [D. Ye, B. Zhu, J. Zhou, arXiv, 2013 (2013), 38 pages], we define the concept of the mixed L p -dual affine surface area for multiple star bodies for all real p ( p ≠ − n ) and establish its monotonicity inequalities and cyclic inequalities. Besides, the Brunn-Minkowski type inequalities of the mixed L p -dual affine surface area for multiple star bodies with two addition are also presented.