相关论文: Norm inequalities related to the matrix geometric …
One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric inequalities for the simplex in $\mathbb{R}^d$ and polytopes…
The main goal of this paper is to discuss the recent advancements of operator means for accretive matrices in a more general setting. In particular, we present the general form governing the well established definition of geometric mean,…
Some rearrangement inequalities for symmetric norms on matrices are given as well as related results for operator convex functions.
We give tight bounds for logarithmic mean. We also give new Frobenius norm inequalities for two positive semidefinite matrices. In addition, we give some matrix inequalities on matrix power mean.
We shall give a refinement of the arithmetic-geometric mean inequality.
Equivalencies of many basic elementary inequalities are given
It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental Arithmetic mean - Geometric mean - Harmonic mean inequality in terms of the means and variance of positive real…
For any positive invertible matrix $A$ and any normal matrix $B$ in $M_{n}({\Bbb C})$, we investigate whether the inequality $ ||A\sharp (B^{*}A^{-1}B)||\geq ||B|| $ is true or not, where $\sharp$ denotes the geometric mean and $||\cdot||$…
We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.
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…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented
We offer a new proof of uniform convexity inequalities for the Finsler manifold of nonpositive curvature taken on the space of positive-semidefinite matrices with the weighted matrix geometric mean defining the geodesic between two points.…
We establish an inequality of different metrics for algebraic polynomials.
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
There are numerous examples in different research fields where the use of the geometric mean is more appropriate than the arithmetic mean. However, the geometric mean has a serious limitation in comparison with the arithmetic mean. Means…
We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…
The concept of Loewner (partial) order for general complex matrices is introduced. After giving the definition of arithmetic, geometric, and harmonic mean for accretive-dissipative matrices, we study their basic properties. An AM-GM-HM…
In this paper we introduce the limit, unique solution of the nonlinear equations, geodesic property, tolerance relations and pinch on the spectral geometric mean for two positive definite operators. We show that the spectral geometric mean…