Related papers: Sharpening Jensen's Inequality
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the…
In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…
The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound.…
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…
In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csisz\'{a}r \cite{csi1} $f-$divergence. A result is established that…
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of…
An inequality, recently proposed by Franson [Phys. Rev. A 54, 3808 (1996)] is analyzed and improved. The inequality connects the change of the expectation value of an observable with the uncertainty of this observable. A strict bound on the…
We introduce a novel parametric family of symmetric information-theoretic distances based on Jensen's inequality for a convex functional generator. In particular, this family unifies the celebrated Jeffreys divergence with the…
The aim of this paper is to introduce several notions of homogenization in various classes of weighted means, which include quasiarithmetic and semideviation means. In general, the homogenization is an operator which attaches a homogeneous…
We extend Dragomir's refinement of Jensen's inequality from the dicrete to the general case, identifying the equality conditions.
Problems pointwise estimates from above functions or its averages often arise in the function theory under known integral restrictions on the growth of this function. We offer an approach to such problems based on the integral Jensen's…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.
In this paper we shall prove a sharpened version of the Finsler-Hadwiger inequality which is a strong generalization of Weitzenbock inequality. After that we give another refinement of this inequality and in the final part we provide some…
We consider the variance of a function of $n$ independent random variables and provide new inequalities which, in particular, extend previous results obtained for symmetric functions in the i.i.d.~setting. For instance, we obtain various…
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using…
We propose new summary statistics for intensity-reweighted moment stationary point processes that generalise the well known J-, empty space, and nearest-neighbour distance distribution functions, represent them in terms of generating…
In this paper, by a concise and elementary approach, we sharpen and generalize Shafer's inequality for the arc sine function, and some known results are extended and generalized.
The purpose of this paper is to provide a random version of Simons' inequality.
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…