An orbitope is the convex hull of an orbit of a point under the action of a compact group. We derive bounds on volumes of sections of polar bodies of orbitopes, extending methods developed in [BB03]. As an application we realize the cone of convex forms as a section of the cone of nonnegative bi-homogeneous forms and estimate its volume. A convex form has to be nonnegative, but it has not been ...

We consider the conic linear program given by a closed convex cone in an Euclidean space and matrix, where vector on right-hand side of inequality constraint defining objective function are subject to change. Using strict feasibility condition, we prove locally Lipschitz continuity obtain some differentiability properties optimal value problem under right-hand-side perturbations. For perturbati...

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

A convex cone metric space is a cone metric space with a convex structure. In this paper, we extend an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings to convex cone metric spaces. Our result generalizes Theorem 2 in [1].

Motivated by applications in financial mathematics, [3] showed that, although L(R+; Ω,F ,P) fails to be locally convex, an analogue to the classical bipolar theorem can be obtained for subsets of L(R+; Ω,F ,P) : if we place this space in polarity with itself, the bipolar of a set of non-negative random variables is equal to its closed (in probability), solid, convex hull. This result was extend...

Motivated by applications in financial mathematics, [3] showed that, although L(R+; Ω,F ,P) fails to be locally convex, an analogue to the classical bipolar theorem can be obtained for subsets of L(R+; Ω,F ,P) : if we place this space in polarity with itself, the bipolar of a set of non-negative random variables is equal to its closed (in probability), solid, convex hull. This result was extend...

The conic structure of the convex cone of non-negative operator convex functions on (0,∞) (also on (−1, 1)) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex cone.