Related papers: Jensen convex functions and doubly stochastic matr…

The two-functional conjecture says that if a function f analytic and univalent in the unit disk maximizes Re{L} and Re{M} for two continuous linear functionals L and M, L is not equal to cM for any c>0, then f is a rotation of the Koebe…

We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…

The Kantorovich function $(x^TAx)(x^T A^{-1} x)$, where $A$ is a positive definite matrix, is not convex in general. From matrix/convex analysis point of view, it is interesting to address the question: When is this function convex? In this…

In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…

This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…

In this work, new inequalities connected with the Steffensen's integral inequality for s-convex functions are proved

Fe{j}\'er and Levin-Ste\v{c}kin inequalities treat integrals of the product of convex functions with symmetric functions. The main goal of this article is to present possible matrix versions of these inequalities. In particular,…

In this paper, we introduce and investigate a class P of continuous and periodic functions on R. The class P is defined so that second-order central differences of a function satisfy some concavity-type estimate. Although this definition…

In this work we extend the characterization of semimartingale functions in Cinlar et al. (1980) to the non-Markovian setting. We prove that if a function of a semimartingale remains a semimartingale, then under certain conditions the…

In the present paper we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms…

We prove a Jensen formula for slice-regular functions of one quaternionic variable. The formula relates the value of the function and of its first two derivatives at a point with its integral mean on a three dimensional sphere centred at…

Let $E$ be a real vector space with dual space $E^*$ and let $C\subset E$ be a convex subset with more than one point. Let $f : C\to\mathbb{R}$ be a function satisfying a mild stability property at 'flat' points of the (relative) boundary…

In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…

In this note functions that transform open segments of a linear space into open segments of another linear space are studied and characterized. Assuming that the range is non-collinear, it is proved that such a map can always be expressed…

We consider convex trace functions $\Phi_{p,q,s} = Trace[ (A^{q/2}B^p A^{q/2})^s]$ where $A$ and $B$ are positive $n\times n$ matrices and ask when these functions are convex or concave. We also consider operator convexity/concavity of…

In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type…

We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the…

Let $(M,d)$ be a separable and complete geodesic space with curvature lower bounded, by $\kappa\in \mathbb R$, in the sense of Alexandrov. Let $\mu$ be a Borel probability measure on $M$, such that $\mu\in\mathcal P_2(M)$, and that has at…

This article gives necessary and sufficient conditions for the dual representation of Rockafellar in (Integrals which are convex functionals. II, Pacific J. Math., 39:439--469, 1971) for integral functionals on the space of continuous…

We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…