Related papers: Matrix inequalities for the difference between ari…
Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type…
We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…
Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…
We complement a recent result of S. Furuichi, by showing that the differences $\sum_{i=1}^n \alpha_i x_i - \prod_{i=1}^n x_i^{\alpha_i}$ associated to distinct sequences of weights are comparable, with constants that depend on the smallest…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that…
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…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
In this paper we have considered two one parametric generalizations. These two generalizations have in articular the well known measures such as: J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric mean divergence. These three…
We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.
An interplay between the sum of certain series related to Harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits…
We investigate improved forms of the Bohr inequality, using the quantity $S_r/\pi$, for analytic selfmaps in class $\mathcal{B}$ of $\mathbb{D}$, where $S_r$ is the area measure of $\mathbb{D}_r$. We then generalize the inequality for…
The main target of this paper is to discuss operator Hermite--Hadamard inequality for convex functions, without appealing to operator convexity. Several forms of this inequality will be presented and some applications including norm and…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated…
One considers certain degenerations of the generic symmetric matrix over a field $k$ of characteristic zero and the main structures related to the determinant $f$ of the matrix, such as the ideal generated by its partial derivatives, the…
In this paper, a general form of integral inequalities of Hermite-Hadamard's type through differentiability for s-Convex function in second sense and whose all derivatives are absolutely continuous are established. The generalized integral…
In the current work, the author present a symbolic algorithm for finding the determinant of any general nonsingular cyclic heptadiagonal matrices and inverse of anti-cyclic heptadiagonal matrices. The algorithms are mainly based on the work…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.