相关论文: A Remark on the Mandl's Inequality
In this paper, we study refinements of some inequalities related to Young inequality for scalar and for operator. As our main results, we show refined Young inequalities for two positive operators. This results refine the ordering relations…
The normalised volume measure on the $\ell_p^n$ unit ball ($1\leq p\leq 2$) satisfies the following isoperimetric inequality: the boundary measure of a set of measure $a$ is at least $cn^{1/p}\tilde{a}\log^{1-1/p}(1/\tilde{a})$, where…
This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…
We establish upper bounds for the distance to finite-dimensional subspaces in inner product spaces and improve some generalisations of Bessel's inequality obtained by Boas, Bellman and Bombieri. Refinements of the Hadamard inequality for…
Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We…
We prove some extensions of Andrews inequality.
We show that for every positive p, the L_p-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. random variables, whose moduli have a nondegenerate distribution with the p-norm one, is comparable to the…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
The original Hotelling-Solomons inequality indicates that an upper bound of |mean - median|/(standard deviation) is 1. In this note, we find a new bound depending on the sample size, which is strictly smaller than 1.
The achievement of this paper is a confutation of the inequality addressed by the Nicolas criterion for the Riemann Hypothesis, carried out after establishing properties of two related sequences. One of them is the product…
We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.
In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.
This note proves a version of Lubell-Yamamoto-Meshalkin inequality for general product measures.
In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.
We improve constants in the Rademacher-Menchov inequality.
We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length be rank-one, as it was shown in [6][L. Shue, B.D.O.…
We consider the problem of finding the set of permutations $r_j$ of $\{1,\cdots , n\}$ such that $\sum_{i=1}^n \prod_{j=1}^k r_j(i)$ is maximized or minimized. While the set of permutations maximizing this value are easily determined,…
A simple method is shown to provide optimal variational bounds on $f$-divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.