Geometric inequalities for anti-blocking bodies

Volume difference inequalities for the projection and intersection bodies

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

New inequalities for star bodies

Some weighted operator geometric mean inequalities

In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...

volume difference inequalities for the projection and intersection bodies

in this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. following this, we establish the minkowski and brunn-minkowski inequalities for volumes difference function of the projection and intersection bodies.

Inequalities for Mixed Complex Projection Bodies

Complex projection bodies were introduced by Abardia and Bernig, recently. In this paper some geometric inequalities for mixed complex projection bodies which are analogs of inequalities for mixed real projection bodies are established.