相关论文: A Singular Value Inequality for Heinz Means

We introduce finite and symmetric Mordell-Tornheim type of multiple zeta values and give a new approach to the Kaneko-Zagier conjecture stating that the finite and symmetric multiple zeta values satisfy the same relations.

In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the…

The celebrated Heinz inequality asserts that $ 2|||A^{1/2}XB^{1/2}|||\leq |||A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}|||\leq |||AX+XB|||$ for $X \in \mathbb{B}(\mathscr{H})$, $A,B\in \+$, every unitarily invariant norm $|||\cdot|||$ and $\nu \in…

We prove some refinements of an inequality due to X. Zhan in an arbitrary complex Hilbert space by using some results on the Heinz inequality. We present several related inequalities as well as new variants of the Corach--Porta--Recht…

We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.

The purpose of this paper is to extend the definition of quasiarithmetic means by taking a strictly monotone generating function instead of a strictly monotone and continuous one. We establish the properties of such means and compare them…

In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.

In this paper, we obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections…

We first prove the following generalization of Schwarz lemma for harmonic mappings. Let $u$ be a harmonic mapping of the unit ball onto itself. Then we prove the inequality $\|u(x)-(1-\|x\|^2)/(1+\|x\|^2)^{n/2} u(0)\|\le U(|x| N)$. By using…

We prove an f-version of Mirsky's singular value inequalities for differences of matrices. This f-version consists in applying a positive concave function f, with f(0)=0, to every singular value in the original Mirsky inequalities.

We prove the existence of gaps between all the different classes of matrix monotone functions defined on an interval, provided the interval is non trivial and different from the whole real line. We then show how matrix monotone functions…

In this paper, the authors establish a new type integral inequalities for differentiable s-convex functions in the second sense. By the well-known H\"older inequality and power mean inequality, they obtain some integral inequalities related…

We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…

We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…

Combinatorial mixed valuations associated to translation-invariant valuations on polytopes are introduced. In contrast to the construction of mixed valuations via polarization, combinatorial mixed valuations reflect and often inherit…

In this article we consider a method of proving a class of inequalities of the form (1). The method is based on the precise approximations of the sine and cosine functions by Maclaurin polynomials of given order. By using this method we…

We prove a classification theorem for Hankel weighing matrices.

We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro-Warschawski class of univalent functions as well as for the closed convex hulls of the convex and…

We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing while…

Let $n \in \N$ and $M_n$ be the algebra of $n \times n$ matrices. We call a function $f$ matrix monotone of order $n$ or $n$-monotone in short whenever the inequality $f(a) \leq f(b)$ holds for every pair of selfadjoint matrices $a, b \in…