Related papers: A Remark on the Mandl's Inequality

Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…

We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between…

Let $\overline{p}(n)$ denote the overpartition funtion. Engel showed that for $n\geq2$, $\overline{p}(n)$ satisfied the Tur\'{a}n inequalities, that is, $\overline{p}(n)^2-\overline{p}(n-1)\overline{p}(n+1)>0$ for $n\geq2$. In this paper,…

Let $A, B$ and $X$ be $n\times n$ matrices such that $A, B$ are positive semidefinite. We present some refinements of the matrix Cauchy-Schwarz inequality by using some integration techniques and various refinements of the Hermite--Hadamard…

The best known upper estimates for the constants of the Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}$ spaces are of the form $\left(\sqrt{2}\right) ^{m-1}.$ We present better estimates which depend on $p$ and $m$. An…

We consider the inhomogeneous Dirichlet problem on product domains. The main result is the asymptotic expansion of the solution in terms of increasing smoothness up to the boundary. In particular, we show the exact nature of the…

The estimate in Bullen's inequality will be extended for continuous functions using the second order modulus of smoothness. A different form of this inequality will be given in terms of the least concave majorant. Also, the composite case…

We establish the optimal lower bound $\gtrsim N$ for counting the number of distinct inner products of pairs from any $N$ given vectors in $\R^2$. Essentially, we lift a related incidence structure defined by inner products in the plane to…

We give lower bounds on the case of worst inhomogeneous approximation.

In this paper we take a probabilistic look at Maclaurin's inequality, which is a refinement of the classical AM-GM inequality. In a natural randomized setting, we obtain limit theorems and show that a reverse inequality holds with high…

We consider the $p$-generalized arithmetic-geometric mean inequality for vectors chosen randomly from the $\ell_p^n$-ball in $\mathbb{R}^n$. In this setting the inequality can be improved or reversed up to a respective scalar constant with…

Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing…

We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the…

Given a large finite point set, $P\subset \mathbb R^2$, we obtain upper bounds on the number of triples of points that determine a given pair of dot products. That is, for any pair of positive real numbers, $(\alpha, \beta)$, we bound the…

We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…

Reference prices have long been studied in applied economics and business research. One of the classic formulations of the reference price is in terms of an iterative function of past prices. There are a number of limitations of such a…

We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear elliptic partial differential equations. In particular, our…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

This paper derives an inequality relating the p-norm of a positive 2 x 2 block matrix to the p-norm of the 2 x 2 matrix obtained by replacing each block by its p-norm. The inequality had been known for integer values of p, so the main…

The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…