Related papers: Gasparyan's Inequality

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

We present a unified strategy to derive Hardy-Poincar\'e inequalities on bounded and unbounded domains. The approach allows proving a general Hardy-Poincar\'e inequality from which the classical Poincar\'e and Hardy inequalities immediately…

The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…

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…

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions…

We examine the efficiency of the mean deviation and Gini's mean difference (the mean of all pairwise distances). Our findings support the viewpoint that Gini's mean difference combines the advantages of the mean deviation and the standard…

A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.

In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.

A simple normal form for Hardy operators is introduced that unifies and simplifies the theory of weighted Hardy inequalities. A straightforward transition to normal form is given that applies to the various Hardy operators and their duals,…

Inequality is an inherent part of our lives: we see it in the distribution of incomes, talents, resources, and citations, amongst many others. Its intensity varies across different environments: from relatively evenly distributed ones, to…

This paper is motivated by an astonishing result of H. Alzer and S. Ruscheweyh published in 2001 in the Proc. Amer. Math. Soc., which states that the intersection of the classes two-variable Gini means and Stolarsky means is equal to the…

To simultaneously overcome the limitation of the Gini index in that it is less sensitive to inequality at the tails of income distribution and the limitation of the inter-decile ratios that ignore inequality in the middle of income…

The discrete isoperimetric inequality states that among all n -gons with a fixed area, the regular n -gon has the least perimeter. We prove analogues of the discrete isoperimetric inequality (involving circumradius or inradius) for cyclic…

We establish a general criterion for the validity of inequalities of the following form: A certain convex combination of the values of a convex function at n points and of its value at a weighted mean of these n points is always greater or…

This note establishes that the opposite Gaussian product inequality (GPI) of the type proved by Russell & Sun (2022a) in two dimensions, and partially extended to higher dimensions by Zhou et al. (2024), continues to hold for an arbitrary…

Hayashi's Pinching Inequality, which establishes a matrix inequality between a semidefinite matrix and a multiple of its "pinched" version via a projective measurement, has found many applications in quantum information theory and beyond.…

We present a refinement, by selfimprovement, of the arithmetic geometric inequality.

We prove a version of the Bombieri--Vinogradov Theorem with certain products of Gaussian primes as moduli, making use of their special form as polynomial expressions in several variables. Adapting Vaughan's proof of the classical…

We present a complete system of inequalities for the inradius, circumradius, and diameter in the $3$-dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius evaluated over $n$-simplices with a common facet…