Related papers: A generalization of an inequality from IMO 2005
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].
We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number $r \in \{1\} \cup [2, \infty)$, positive semi-definite matrices $A_i,\…
We improve an isoperimetric inequality due to Panos Papasoglu. We also generalize this inequality to the Finsler case by proving an optimal Finsler version of the Besicovitch's lemma which holds for any notion of Finsler volume.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
In the present note a generalization of Borel-Cantelli Lemma is proposed.
Fano's inequality is one of the most elementary, ubiquitous, and important tools in information theory. Using majorization theory, Fano's inequality is generalized to a broad class of information measures, which contains those of Shannon…
A proof of Sendov's conjecture is given.
If $P$ is an orthogonal projection defined on an inner product space $\mathcal{H}$, then the inequality $$ |\langle Px, y\rangle|\leq \frac12 [\|x\|\|y\|+|\langle x, y\rangle|] $$ fulfills for any $x,y \in \mathcal{H}$ (see \cite{Dra16}).…
We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.
A proof of Smale's mean value conjecture from 1981 is given.
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.
We prove a stability version of the Pr\'ekopa-Leindler inequality.
This note provides the generalization of a remarkable inequality by A. C. Ponce whose consequences are essential in several fields, as Characterization of Sobolev Spaces or Nonlocal Modelization.
We provide a new characterization of the logarithmic Sobolev inequality.
The duality is a fundamental property of the finite multiple harmonic sums (MHS). In this paper, we prove a duality result for certain generalizations of MHS which appear naturally as the differences of MHS. We also prove a formula for the…
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…
A sharp quantitative polygonal isoperimetric inequality is obtained.
The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.
In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmetic-geometric mean.