相关论文: Selfimprovemvent of the inequality between arithme…
We provide a new characterization of the logarithmic Sobolev inequality.
We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.
We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in $\R^d$, $d \geq 2$. In particular, we derive upper bounds on Riesz means of order $\sigma \geq 3/2$, that improve the sharp Berezin inequality…
The purpose of this paper is to extend the definition of quasiarithmetic means by taking a strictly monotone generating function instead of a strictly monotone and continuous one. We establish the properties of such means and compare them…
The main goal of this article is to present several quadratic refinements and reverses of the well known Heinz inequality, for numbers and matrices, where the refining term is a quadratic function in the mean parameters. The proposed idea…
In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.
Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between…
Our main result is an abstract good-$\lambda$ inequality that allows us to consider three self-improving properties related to oscillation estimates in a very general context. The novelty of our approach is that there is one principle…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable…
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem,…
The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…
We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\'e…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
A sharp quantitative polygonal isoperimetric inequality is obtained.
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
The main result of this paper supports a conjecture by C. P\'erez and E. Rela about a very recent result of theirs on self-improving theory. Also, we extend the conclusions of their theorem to the range $p<1$. As an application of our…
We improve constants in the Rademacher-Menchov inequality.