相关论文: A matrix subadditivity inequality for f(A+B) and f…

We present some operator inequalities for positive linear maps that generalize and improve the derived results in some recent years. For instant, if $A$ and $B$ are positive operators and $m,m^{'},M,M^{'}$ are positive real numbers…

We review some convexity inequalities for Hermitian matrices an add one more to the list.

We improve the operator Kantorovich inequality as follows: Let $A$ be a positive operator on a Hilbert space with $0<m\le A \le M$. Then for every unital positive linear map $\Phi$, \[\Phi(A^{-1})^2\le (\frac{(M+m)^2}{4Mm})^2\Phi(A)^{-2}.\]…

In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function $f:\mathbb R^n\rightarrow[0,\infty)$ and any concave function $h:L\rightarrow\mathbb [0,\infty)$, where $L$ is the epigraph of…

We prove two inequalities for the Mittag-Leffler function, namely that the function $\log E_\alpha(x^\alpha)$ is sub-additive for $0<\alpha<1,$ and super-additive for $\alpha>1.$ These assertions follow from two new binomial inequalities,…

Given an integer $a\ge 1$, a function $f: \mathbb{R}\to \mathbb{R}$ is said to be $a$-subadditive if $$ f(ax+y) \le af(x)+f(y) \,\,\,\text{ for all }x,y \in \mathbb{R}. $$ Of course, $1$-subadditive functions (which correspond to ordinary…

In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two…

We prove a version of the Beurling-Malliavin multiplier theorem. This version is formulated here in a simplified form. Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ be a pair of subharmonic functions on the complex plane $\mathbb C$…

The classical Perron-Frobenius theory asserts that for two matrices $A$ and $B$, if $0\leq B \leq A$ and $r(A)=r(B)$ with $A$ being irreducible, then $A=B$. This was recently extended in Bernik et al. (2012) to positive operators on…

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds. In this paper, we…

Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times…

Recently the behavior of operator monotone functions on unbounded intervals with respect to the relation of strictly positivity has been investigated. In this paper we deeply study such behavior not only for operator monotone functions but…

Let A= (a_{ij}) be a symmetric non-negative integer 2k x 2k matrix. A is homogeneous if a_{ij} + a_{kl}=a_{il} + a_{kj} for any choice of the four indexes. Let A be a homogeneous matrix and let F be a general form in C[x_1, \dots x_n] with…

There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasing functions. Leveraging this distinction, we introduce…

We show the following result: Let $A$ be a positive operator satisfying $0<m{{\mathbf{1}}_{\mathcal{H}}}\le A\le M{{\mathbf{1}}_{\mathcal{H}}}$ for some scalars $m,M$ with $m<M$ and $\Phi $ be a normalized positive linear map, then \[\Phi…

We analyze the role played by $n$-convexity for the fulfillment of a series of linear functional inequalities that extend the Hornich-Hlawka functional inequality, $f\left( x\right) +f\left( y\right) +f\left( z\right) +f\left( x+y+z\right)…

Let $\sigma$ be a non-trivial operator mean in the sense of Kubo and Ando, and let $OM_+^1$ the set of normalized positive operator monotone functions on $(0, \infty)$. In this paper, we study class of $\sigma$-subpreserving functions $f\in…

We describe recent work of Kim in arXiv:1210.5190 to show that operator convex functions associated with quasi-entropies can be used to prove a large class of new matrix inequalities in the tri-partite and bi-partite setting by taking a…

In this paper, we solve the following tri-additive $s$-functional inequalities \begin{eqnarray}\label{0.1} && \nonumber \| f(x+y, z-w, a+b) + f(x-y, z+w, a-b) \\ && \nonumber\qquad -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\|…

We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for fully resolving a conjecture of Harwitz and Sloane, commonly…