Related papers: Vector-Valued Maclaurin Inequalities
In this paper we study an autocorrelation inequality proposed by Barnard and Steinerberger. The study of these problems is motivated by a classical problem in additive combinatorics. We establish the existence of extremizers to this…
The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a result of our studies for mathematical properties on entropy and divergence, we give new bounds for the Tsallis…
We give a new recurrent inequality on a class of vertex Folkman numbers.
We give a survey of classical and recent results on sharp constants and symmetry/asymmetry of extremal functions in $1$-dimensional functional inequalities.
In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.
We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential Calogero--Degasperis equation and generalizations of the Schwarzian KdV equation. Equations and differential substitutions under…
This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type…
This paper introduces vector copulas associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation, and establishes a vector version of Sklar's theorem. The latter provides a…
Equivalencies of many basic elementary inequalities are given
This paper presents a number of Kantorovich type integral inequalities involving tensor products of continuous fields of bounded linear operators on a Hilbert space. Kantorovich type inequality in which the product is replaced by an…
In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell.…
The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or…
We establish new and stronger inequality of Clarke-Ledyaev type by direct construction.
We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term…
We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.
In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.
In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…
Our main result is the proof of an inequality between the spectral numbers of a Lagrangian and the spectral numbers of its reductions, in the opposite direction to the classical inequality (see e.g [Vit92]). This has applications to the…
An elliptic analogue of the $q$ deformed Knizhnik-Zamolodchikov equations is introduced. A solution is given in the form of a Jackson-type integral of Bethe vectors of the XYZ-type spin chains.