On some new Hilbert-type inequalities

In the present paper we establish some new inequalities similar to extensions of Hilbert’s double-series inequality and give also their integral analogues. Our results provide some new estimates to these types of inequalities.     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-mixed intersection bodies and star duality

The paper extends the two notions of the dual mixed volumes and L _p -intersection body to q-dual mixed volumes and L _p -mixed intersection body, respectively. Inequalities for the star dual of L _p -mixed intersection bodies are established.     

Radial Blaschke–Minkowski homomorphisms and volume differences

In this paper we establish Minkowski, Brunn–Minkowski, and Aleksandrov-Fenchel type inequalities for volume differences of radial Blaschke–Minkowski homomorphisms.