Related papers: Sharpening Jensen's Inequality
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.
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.
We give tight bounds for logarithmic mean. We also give new Frobenius norm inequalities for two positive semidefinite matrices. In addition, we give some matrix inequalities on matrix power mean.
We derive a number of sharp upper bounds for the deficit in the Alexandrov-Fenchel inequality using a weighted Minkowski integral formula and an integral formula for the deficit in Jensen's inequality. Our estimates yield results under…
Let $I$ and $J$ be two intervals, and let $f, g: I \rightarrow \mathbb{R}$. If for any points $a$ and $b$ in $I$ and any positive numbers $p$ and $q$ such that $p + q = 1$, we have \begin{align} \nonumber p f(a) + q f(b) + g(pa + qb) \in J,…
We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are oriented (asymmetric) distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as…
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…
This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained proofs. Our results are sharp and minimizers are obtained in…
We explore the applications of our previously established likelihood-ratio method for deriving concentration inequalities for a wide variety of univariate and multivariate distributions. New concentration inequalities for various…
A refinement of so-called fast Johnson-Lindenstrauss transform, due to Ailon and Chazelle (2006), and Matou\v{s}ek (2008), is proposed. While it preserves the time efficiency and simplicity of implementation of the original construction, it…
In recent study of partial differential equations (PDEs) with random initial data and singular stochastic PDEs with random forcing, it is essential to study the regularity property of various stochastic objects. These stochastic objects are…
We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function…
In this work, we investigate the question of how knowledge about expectations $\mathbb{E}(f_i(X))$ of a random vector $X$ translate into inequalities for $\mathbb{E}(g(X))$ for given functions $f_i$, $g$ and a random vector $X$ whose…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
In this paper, we provide a new and sharper bound for the Legendre coefficients of differentiable functions and then derive a new error bound of the truncated Legendre series in the uniform norm. The key idea of proof relies on integration…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function.…