In this article, we establish Minkowski, Brunn-Minkowski and Aleksandrov-Fenchel type inequalities for differences of quermass-and dual quermassintegrals of mixed Blaschke-Minkowski and mixed radial Blaschke-Minkowski homomorphisms.

In this paper, some dual Brunn-Minkowski inequalities are established for intersection bodies for the harmonic Blaschke additions and p-radial additions.

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In this paper, the monotonic results of the functions x c |ψ (n) (x + β)| and xψ (n+1) (x + β)/ψ (n) (x + β) are established. Several by-products are obtained. Moreover, we prove that the function dψ (ln x) dx is completely monotonic. (2000): 33B15, 26A48. Mathematics subject classification