  By calculating the first order variation of the dual mixed volumes, we put
forward a new concept Orlicz multiple dual mixed volumes. The classical dual
mixed volumes and dual Aleksandrov-Fenchel inequality are generalized to the
Orlicz space. We establish dual Orlicz Aleksandrov-Fenchel inequality and a new
concept of Lp multiple dual mixed volume and Lp dual Aleksandrov Fenchel
inequality are first derived here, too. The dual Aleksandrov-Fenchel inequality
and the Lp-dual Aleksandrov-Fenchel inequality are all special cases of the
dual Orlicz-Aleksandrov-Fenchel inequality. As an application, a new dual
Orlicz-Brunn-Minkowski inequality for the Orlicz harmonic addition is also
established.
