Some Inequalities For Dual Orlicz Mixed Quermassintegral

We study the dual Orlicz mixed Quermassintegral.For arbitrary monotone continuous function ?,the dual Orlicz radial sum and dual Orlicz mixed Quer-massintegral are introduced.Then the dual Orlicz-Minkowski inequality and dual Orlicz-Brunn-Minkowski inequality for dual Orlicz mixed Quermassintegral are ob-tained.These inequalities are just the special cases of their Lp analogues(including cases-?<p<0,p = 0,0<p<1,p=1,and 1<p<+?).These inequalities for ? = logt are related to open problems including log-Minkowski problem and log-Brunn-Minkowski problem.Moreover,the equivalence of the dual Orlicz-Minkowski inequality for dual Orlicz mixed Quermassintegral and dual Orlicz-Brunn-Minkowski inequality for dual Orlicz mixed Quermassintegral is shown.