Related papers: A Note On Andrews Inequality

Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two…

We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.

This note is the follow up to a paper by M. Waldschmidt.

We extend the fundamental normality test due to Carath\'eodory in the sense of shared functions.

In this paper,we will give an easy example to satisfy that we can not conclude CDE' Inequality just from the CD Inequality.

In this note, we present an information diffusion inequality derived from an elementary argument, which gives rise to a very general Fano-type inequality. The latter unifies and generalizes the distance-based Fano inequality and the…

We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some…

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

In this note, we offer some relations and congruences for an interesting $spt$-type function.

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type.

In this note we extend a theorem from [13] about uniform circle random coverings

In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…

By using a Hedberg-type inequality, the Adams trace inequality is extended from Lebesgue spaces to product Morrey spaces.

We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].

We prove a variation of Gronwall's lemma.

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…

A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities.

We improve the classical discrete Hardy inequality \begin{equation*}\label{1} \sum _{{n=1}}^{\infty }a_{n}^{2}\geq \left({\frac {1}{2}}\right)^{2} \sum _{{n=1}}^{\infty }\left({\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}\right)^{2},…