相关论文: A Note On Mixed Mean Inequalities
In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of…
Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.
In this note we prove Jensen-type inequality for certain non-convex functions. We apply our idea to prove some inequalities which were suggested at some high-level math olympiades.
We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.
In this paper we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of operator Acz\'el inequality dealing with the weighted geometric mean.
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…
We prove some extensions of Andrews inequality.
At the heart of convex geometry lies the observation that the volume of convex bodies behaves as a polynomial. Many geometric inequalities may be expressed in terms of the coefficients of this polynomial, called mixed volumes. Among the…
For two positive real numbers $x$ and $y$ let $H$, $G$, $A$ and $Q$ be the harmonic mean, the geometric mean, the arithmetic mean and the quadratic mean of $x$ and $y$, respectively. In this note, we prove that \begin{equation*} A\cdot G\ge…
In this article, we present the best possible upper and lower bounds for the Neuman-S\'andor mean in terms of the geometric combinations of harmonic and quadratic means, geometric and quadratic means, harmonic and contra-harmonic means, and…
A positive real interval, [a, b], can be partitioned into sub-intervals such that sub-interval widths divided by sub-interval "average" values remains constant. That both Arithmetic Mean and Geometric Mean "average" values produce constant…
We explore the concentration properties of the ratio between the geometric mean and the arithmetic mean, showing that for certain sequences of weights one does obtain concentration, around a value that depends on the sequence.
In this note, we provide with a simple example to show a defect in the definition of the geometric mixing scale, and then introduce an improved scale, called as the strong geometric mixing scale. The main theorem in this note is the…
We prove a multivariate version of Hoeffding's inequality about the distribution of homogeneous polynomials of Rademacher functions. The proof is based on such an estimate about the moments of homogeneous polynomials of Rademacher functions…
We investigate several instances of the Hadamard inequality in the mean in two dimensions. As a consequence, we prove the uniqueness of minimizers of an integral functional with a polyconvex integrand, subject to mixed Dirichlet and Neumann…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
In this work, an extension of the generalized mixed Schwarz inequality is proved. A companion of the generalized mixed Schwarz inequality is established by merging both Cartesian and Polar decompositions of operators. Based on that some…
This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to $L^p$-improving inequalities for Radon-like transforms over polynomial submanifolds of intermediate…
For $n$ positive numbers ($a_k$, $1\leq k \leq n$), enhanced inequalities about the arithmetic mean ($A_n \equiv \frac{\sum_ka_k}{n}$) and the geometric mean ($G_n\equiv \sqrt[n]{\Pi_ka_k}$) are found if some numbers are known, namely,…
We present some results concerning the $l^p$ norms of weighted mean matrices. These results can be regarded as analogues to a result of Bennett concerning weighted Carleman's inequalities.