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In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the…
This article discusses the main aspects related to Bell's inequality, both theoretical and experimental. A new derivation of Bell's inequality is also presented, which stands out for its mathematical simplicity. The exposition is mainly…
We make a careful analysis of Bohr's inequality, in the line started by Kayumov and Ponnusamy, where some extra summand (depending on the function) is added in the right-hand side of the inequality. We analyse the inequality when smaller…
Fe{j}\'er and Levin-Ste\v{c}kin inequalities treat integrals of the product of convex functions with symmetric functions. The main goal of this article is to present possible matrix versions of these inequalities. In particular,…
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of…
This paper surveys some of our recent progress on Hardy-type inequa\-lities which consist of a well-known topic in Harmonic Analysis. In the first section, we recall the original probabilistic motivation dealing with the stability speed in…
The primary objective of this paper is to establish several sharp versions of improved Bohr inequalities, refined Bohr inequalities, and Bohr-Rogosinski inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings…
In the paper, the authors establish some best approximation formulas and inequalities for Wallis ratio. These formulas and inequalities improve an approximation formula and a double inequality for Wallis ratio recently presented in ``S.…
The aim of this paper is to present an abstract and general approach to jump inequalities in harmonic analysis. Our principal conclusion is the refinement of $r$-variational estimates, previously known for $r>2$, to end-point results for…
This note is concerned with lower tail estimates for product measures. Some improved deviation inequalities are obtained for functions satisfying some regularity and monotonicity assumptions. The arguments are based on semigroup…
This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…
We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.
The function $ \tan(\pi x / 2) / (\pi x / 2) $ is expanded into a Laurent series of $ 1 - x^2 $, where the coefficients are given explicitly as combinations of zeta function of even integers. This is used to achieve a sequence of upper and…
In this paper, by estimating the weight coefficient effectively, we establish an improvement of a Hardy-Hilbert type inequality proved by B.C. Yang, our main tool is Euler-Maclaurin expansion for the zeta function. As applications, some…
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with…
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy-Rellich…
Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing…
The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite…