Related papers: Gasparyan's Inequality
In this paper we further develop a Grassmannian technique used to prove results about very general hypersurfaces and present three applications. First, we provide a short proof of the Kobayashi Conjecture given previous results on the…
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that…
The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.
The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…
We shall discuss a higher-rank Khovanskii-Teissier inequality, generalizing a theorem of Li. In the course of the proof, we develop new Hodge-Riemann bilinear relations in certain mixed settings, which in themselves slightly extend the…
This document comes as supplementary material of the paper Stability in Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a number of classical or elementary statements concerning constants and inequalities for…
The notion of "super convex spaces" generalizes the idea of convex spaces by replacing finite affine sums with countable affine sums. Using this notion permits a very elegant approach for analysis of the Giry monad on standard measurable…
We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.
In this note, we present several inequalities in the context of pattern containment, utilizing elementary applications of the Fortuin-Kasteleyn-Ginibre (FKG) inequality and Shearer's lemma.
We introduce some symmetric homogeneous means, and then show unitarily invariant norm inequalities for them, applying the method established by Hiai and Kosaki. Our new inequalities give the tighter bounds of the logarithmic mean than the…
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or R\'enyi entropies. The proof is based on a…
In this expository paper, we discuss a unified framework for proving various geometric inequalities, based on the so-called Alexandrov-Bakelman-Pucci technique. Examples include Cabr\'e's proof of the classical isoperimetric inequality in…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
In this paper authors establish the two sided inequalities for the following two new means $$X=X(a,b)=Ae^{G/P-1},\quad Y=Y(a,b)=Ge^{L/A-1}.$$ As well as many other well known inequalities involving the identric mean $I$ and the logarithmic…
Equivalencies of many basic elementary inequalities are given
In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite…