相关论文: DDVV-type inequality for Hermitian matrices

Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed…

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard type inequality for nonconvex functions whose second derivatives absolute values are \phi-convex, log-\phi-convex, and quasi-\phi-convex.

Let $N$ be a weakly unitarily invariant norm (i.e. invariant for the coadjoint action of the unitary group) in the space of skew-Hermitian matrices $\mathfrak{u}_n(\mathbb C)$. In this paper we study the geometry of the unit sphere of such…

A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…

We establish the converse of Weyl's eigenvalue inequality for additive Hermitian perturbations of a Hermitian matrix.

In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…

In this paper, we establish new some Hermite-Hadamard's type inequalities of convex functions of 2-variables on the co-ordinates.

We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…

In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of…

The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class - the so-called Legendre transformations - were introduced by Dubrovin.…

In this paper, we obtain some Hermite-Hadamard type inequalities for functions whose third derivatives in absolute value are preinvex and prequasiinvex.

In this paper, some new integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions are established and some applications to special means of positive real numbers are also given.

Popoviciu's inequality is extended to the framework of h-convexity and also to convexity with respect to a pair of quasi-arithmetic means. Several applications are included.

An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutators of the respective matrices. The procedure is shown to…

The article gives a necessary and sufficient condition for a Frobenius manifold to be a CDV-structure. We show that there exists a positive definite CDV-structure on any semi-simple Frobenius manifold. We also compare three natural…

Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair $(A,B)$ we provide a normal form with a minimal number of independent parameters to which all pairs of…

In this paper, we establish several new convex dominated functions and then we obtain new Hadamard type inequalities.

Dark equations are defined as some kinds of integrable couplings with some fields being homogeneously and linearly coupled to others. In this paper, dark equations are extended in several aspects. Taking the Korteweg-de Vrise (KdV) equation…

We construct some explicit quasihomogeneous algebraic solutions to the associativity (WDVV) equations by using analytical methods of the finite gap integration theory. These solutions are expanded in the uniform way to non-semisimple…

In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.