Related papers: Conic structure of the non-negative operator conve…

We investigate the convexity property on $(0,1)$ of the function $$f_a(x)=\frac{{\cal K}{(\sqrt x)}}{a-(1/2)\log(1-x)}.$$ We show that $f_a$ is strictly convex on $(0,1)$ if and only if $a\geq a_c$ and $1/f_a$ is strictly convex on $(0,1)$…

Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f: D\to \mathbf{R}\cup \{+\infty\}$ is convex if and only if for all $x,y \in D$ there exists $\alpha=\alpha(x,y) \in (0,1)$ such…

We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main…

In this paper we give a characterization of all order isomorphisms on some classes of convex functions. We deal with the class $Cvx(K)$ consisting of lower-semi-continuous convex functions defined on a convex set $K$, and its subclass…

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset…

We construct $Q$-curvature operators on $d$-closed $(1,1)$-forms and on $\overline{\partial}_b$-closed $(0,1)$-forms on five-dimensional pseudohermitian manifolds. These closely related operators give rise to a new formula for the scalar…

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 our previously developed methods. As an application we realize the…

The paper is devoted to a study of the cone $\cop$ of copositive matrices. Based on the known from semi-infinite optimization concept of immobile indices, we define zero and minimal zero vectors of a subset of the cone $\cop$ and use them…

In this paper, we describe the structural properties of the cone of $\mathcal{Z}$-transformations on the second order cone in terms of the semidefinite cone and copositive/completely positive cones induced by the second order cone and its…

Tensor products of convex cones have recently come up in different areas, ranging from functional analysis and operator theory to approximation theory and theoretical physics. However, most of the existing literature focuses either on…

We show that the symmetrized product $AB+BA$ of two positive operators $A$ and $B$ is positive if and only if $f(A+B)\leq f(A)+f(B)$ for all non-negative operator monotone functions $f$ on $[0,\infty)$ and deduce an operator inequality. We…

We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above,…

In this paper we introduce and study a class of structured set-valued operators which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued…

A recent article Li and Lv considered contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in certain cases where the speed is a function of a degree-one…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to offer a survey on fundamental operations for various kinds of discrete…

We prove conditions for the existence of a continuous linear right inverse for a surjective convolution operator in spaces of germs of analytic functions on convex subsets of the complex plane. Considered convex sets have a countable…

A convex optimization problem in conic form involves minimizing a linear functional over the intersection of a convex cone and an affine subspace. In some cases, it is possible to replace a conic formulation using a certain cone, with a…

In this note, as a particular case of a more general result, we obtain the following theorem: Let $\Omega\subseteq {\bf R}^n$ be a non-empty bounded open set and let $f:\overline {\Omega}\to {\bf R}^n$ be a continuous function which is…

In this paper, which is a sequel of [BKLV], we study the convex-geometric properties of the cone of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. We introduce and study the Abel-Jacobi faces, related to…